Yo lemme tell you about Casts.
Each weapon comes with its own normal attack and flourish, which the boons of the gods can modify the properties of but never outright change. Casts, however, do not follow this rule. Zagreus begins the game with one Bloodstone, which deals 50 damage when cast at someone, and which then embeds in them. This can be modified with two pairs of Mirror of Night talents, but every run you do, Zagreus will always begin play with that option. As such, your Cast is a constant benefit that can overcome the flaws of your weapon of choice.
With this in mind, it's time to consider the boons of the various gods which modify these casts. Some boons can modify the casts further, which will be indicated as well.
Zeus
Electric Shot is a very straightforward modifier for your cast: just bumps base damage up to 60 and lets the shot bounce between enemies. This is a bit of a mixed blessing if you're relying on embedding casts for Blood debuffs, because the chain effect, while accurate, can miss. This makes it better for Infernal Soul rather than Stygian Soul, because if it DOES miss, just grab the Bloodstone and cast again. Like the basic cast, Electric Shot is a fine addition to most loadouts, able to function well at long or short ranges.
Zeus has the boon Lightning Rod (Artemis duo) that makes those discarded casts all the more effective by calling lightning down around them, but that doesn't really modify the cast itself. The only other boon that modifies Electric Shot is Storm Lightning, which lets it bounce more times. I don't find that to be incredibly vital, but it is one of the prerequisites for the legendary boon Splitting Bolt, if you really want to chain some damage everywhere. There's a few duo boons for modifying other casts: Lightning Phalanx (Athena duo) and Scintillating Feast (Dionysus duo), but we'll cover those for those specific gods.
Poseidon
Another basic boon, Flood Shot bumps the base damage up to 60 and makes the cast explode in a wave of knockback. The only thing keeping this from being a more generalist-option than Electric Shot is the knockback making it hard to spam multiple casts without a nice convenient wall, and that the knockback can prove troublesome to melee characters, but don't let either of those things stop you from choosing Flood Shot.
Poseidon has a number of boons to modify casts, although only one (Mirage Shot, an Artemis duo) applies to any cast. The rest all modify Flood Shot. Curse of Drowning (Ares duo) turns it into a series of close-range pulses, making it amazing for long-range builds that need a last-ditch defense or for close-range builds that think dodging is for weaklings. Blizzard Shot (Demeter duo) instead turns into a much slower, piercing shot that sheds ice everywhere, suiting it much more to close-range fighters who can get one foe hit with the same cast multiple times. In either case, your cast no longer embeds, so plan accordingly.
Athena
Phalanx Shot is a much larger change to your cast, literally. The base damage is much higher at 85, and the projectile is larger and deflects while in flight, but it also starts out moving slower and accelerates as it goes. Still, it's another fine choice for most any builds: melee builds want it for deflecting ranged foes, ranged builds want it for spike damage up close where the shot speed is a non-issue.
Athena gets two boons that modify casts, both duos. Parting Shot (Aphrodite duo) grants all casts the ability to backstab and a bonus to backstab damage, while Lightning Phalanx (Zeus duo) grants the Phalanx Shot the ability to chain between targets. Lightning Phalanx is ridiculously good, because again, the rule of thumb for Deflects is "give it a big and active hitbox" and letting the slow-but-accelerating Phalanx Shot persist by chaining can only mean good things.
Aphrodite
Aphrodite gets Crush Shot, which has the second-highest base damage on a Cast at 90, but also turns it from a projectile into a short-range wave (and inflicts Weak because Aphrodite). This means that Crush Shot should really only be taken by long-range builds who need a good way to handle enemies up close in a pinch. Melee builds should probably give it a miss, and instead take almost any other Aphrodite boon (unless you like dying to ten thousand Flame Wheels, in which case woooo spike damage!)
Aphrodite has three boons for modifying casts. Parting Shot (Athena duo) is covered above. Blown Kiss modifies Crush Shot specifically, giving it a bonus on undamaged enemies and barely extending its range, hardly enough to justify using it on a melee weapon. The other one, Cold Embrace (Demeter duo) modifies the Demeter cast, and will be discussed there.
Artemis
True Shot, like almost every other Artemis boon, is just solid and effective. Base of 70 damage with a 10% crit chance, and it homes in on enemies and flies faster. While it's one of the weaker casts for dealing with large crowds of enemies, it's still a perfectly solid cast, especially for melee builds. Ranged builds tend to have better options for covering close encounters, though.
Artemis has probably the most boons in the game for modifying casts or Bloodstones in whatever way, so let's go about that now. First, the non-duo modifiers. Exit Wounds lets Bloodstones deal damage when dislodged, which is cheater-level on a Poseidon sword, decent if you have Quick Reload, and basically useless in all other cases. Support Fire lets you fire off an extra arrow when you cast or hit with Attack/Special, but that's mostly being mentioned for inclusivity, since Casts fire off infrequently enough for that to be useful here. Fully Loaded is Artemis' legendary boon, and it grants two extra Bloodstones, which obviously helps you spam your cast of choice way more often, and is therefore VERY GOOD if you're using casts regularly.
Two of Artemis' duo boons for casts have been detailed above, specifically Mirage Shot (Poseidon) and Lightning Rod (Zeus). Her other duo boons modify specific casts: either Hunting Blades (Ares duo) for Ares' cast, or Crystal Clarity (Demeter duo) for Demeter's cast.
Ares
Slicing Shot is the first of the casts that does not embed, instead procuring an active effect while out. In this case, it creates a Blade Rift, that deals a base of 20 damage for every hit it scores on an enemy. Blade Rifts move slowly, however, so by default they're best used on large, slow targets that won't get out of the way, or against weak targets that will blunder headfirst into it and instantly die. Given the slow movement speed, it's ideal for ranged builds as a good option for handling close-range targets.
Ares has three non-duo boons specifically for modifying Blade Rifts (which his Dash and Call can also produce). Black Metal improves the area of effect, Engulfing Vortex improves the duration and draws nearby foes into them, and the legendary Vicious Cycle increases the damage dealt with each consecutive strike from a Blade Rift. All three of these should be serious considerations if you plan to make any use of Blade Rifts whatsoever, although they all work best on your cast, of course.
Ares also has three duo boons for modifying casts, each of which requires a specific cast. Curse of Drowning (Poseidon duo), as above, only works on Flood Shot, and both Hunting Blades (Artemis duo) and Freezing Vortex (Demeter duo) only effect Slicing Shot. Hunting Blades increases the speed of the cast and causes it to home in on enemies, improving its use mid-range and against less-immobile foes. Freezing Vortex shrinks the area and speed of the cast (and uniquely, increasing the boon's level offsets these penalties), but causes it to inflict Chill with each strike, which is EXTREMELY worth the downsides. It's much harder for a Chilled enemy to escape a Blade Rift, after all. Now, if only those two boons could stack...
Dionysus
Now, I know what you're thinking. Dionysus is a weak god that only uses Hangover effects which aren't very good unless you overinvest in Dionysus boons. Ignore all of that, because Dionysus has the secret best cast in the game. Trippy Shot lobs an arcing bomb that deals 100 base damage (wow!) AND creates a cloud of Festive Fog where it lands. Festive Fog periodically stuns enemies in the area, making them easy pickings for really anyone. Given the similarity to the rail's special, I can't really recommend Trippy Shot for the rail, but it's a solid companion for most any other weapon if you're ready to sacrifice attack speed for big area damage.
Dionysus has a few personal boons that modify Trippy Shot. High Tolerance grants Zagreus some pretty solid damage resistance while standing in Festive Fog, while the legendary Black Out causes Festive Fog to amplify the damage taken by Hungover foes. Both pretty nice effects, maybe a little situational, of course, but the secret power of Trippy Shot doesn't lie there.
No, it lies with the duo boons. Scintillating Feast (Zeus duo) causes lightning strikes to pepper any area with Festive Fog, gaining all the benefits of Zeus' lightning-specific boons in the process. Ice Wine (Demeter duo) changes the cast from an arcing projectile to an instant explosion, increases the damage, and makes it inflict Chill. And unlike Slicing Shot, both of these boons can stack. I am now accepting names for this cast build: the current champion is Fission Vodka Bomb.
Demeter
Finally, we have Demeter, saddled with what is widely considered the weakest Cast in the game: Crystal Beam. Crystal Beam deploys the Bloodstone as a turret for 5 seconds that fires a laser, slowly tracking enemies and dealing 8 damage every fifth of a second. Compare that to basically any other cast, and it doesn't look great. The damage from an optimally-placed base-damage Crystal Beam caps out at 200, but that's assuming whatever you're aiming at stays completely put. Crystal Beam tends to come off as a weaker Slicing Shot, trading the raw damage against slow enemies for mid-range potential. It gets stronger if you apply Chill to enemies, since that slows them down and makes the tracking less of an issue, but it's still not great on its own.
Like the other gods with heavily-unique casts, Demeter gets boons specifically for Crystal Beam, although one boon applies to any cast; namely Snow Burst, which causes Zagreus to emit a close-range pulse of 40 damage with Chill on top whenever he casts. Glacial Glare improves the duration and causes the Crystal Beam to inflict Chill, which means if it DOES get a lock on an enemy, it'll likely stay locked on.
Demeter also gets a large amount of duo boons for modifying casts. We've already seen Blizzard Shot (Poseidon duo), Ice Wine (Dionysus duo), and Freezing Vortex (Ares duo), and all of them are great and good and I like them. For modifying Crystal Beam, you either get Crystal Clarity (Artemis duo) to improve the tracking and damage, although fast enemies can still avoid it, or Cold Embrace (Aphrodite duo) which improves the duration by 4 seconds, boosts the damage, and forces the Crystal Beam to aim at Zagreus. Cold Embrace is especially handy against Greatshields or Theseus, since you can park all your casts on one side, move to the other, and flank your target.