Sword:
Nemesis - Pretty plain (i.e. similar to the normal playstyle you're used to). A solid normal attack build with lots of Specials cycled in. If you don't like normal sword, this one won't change your mind. Particularly shines with Artemis on attack for lots of crit.
Poseidon - Departure. Strongly emphasizes cast-based builds in particular, and changes up your rhythms to maximize that. Artemis's "Exit Wounds" boon is very good if not semi-required. Keep in mind that you super-duper-shouldn't get casts that don't stick in enemies (Dionysus, Demeter, Ares; Zeus sticks but is finicky what with its bouncing)
Spear:
Achilles - Moderate departure from normal play; the rush adds a lot of mobility to the kit, and gives a rare boost to cast (or attack, ofc) damage. My preference.
Hades - Plain. Emphasizes the spin a lot by buffing it and if you like playing with that, but doesn't change up the kit much beyond that.
Shield:
Chaos - Plain or moderate departure; emphasizes lots of blocking and charging to get the extra shields, so it benefits if you already like to block and rush a lot. Needs particular boons on shield to really shine, but up to 5 shields at a time can do some damage, I guess.
Zeus - Huge departure from normal playstyle, probably the biggest of any normal aspect. Sends a slow spinning saw-disc out to sit or be called back manually. It's a little finicky, but can do AMAZING damage with good positioning (protip: use the shield's knockback to push enemies into it!) Put Zeus's boon on special and it's insanely powerful. One of my top 2 or 3 favorite aspects in the game.
Bow:
Chiron - Big departure, in that it redefines your attack rhythms (attack-special-special, repeat). Extremely powerful single-target damage; attack-special-special absolutely melts enemies but it's a little weak on AoE (so just get a cast imo). Another of my top 3 aspects. Typically my recommendation for "first aspect to power up" (if you like the bow).
Hera - Moderate departure in that you lose your cast entirely, but your bow attacks are otherwise the same (albeit empowered by the casts ofc, so it emphasizes powerful attack shots).
Fists:
Talos - Moderate departure. Magnetic cutter is very good - Draws enemies in, giving more control/mobility to the short-range fists; also boosts attack and cast damage nicely.
Demeter - Plain. I don't get this one. Strong focus on huge special attacks after a few punch combos, but 12 attacks is a weird number to base that on; feels arhythmical.
Rail:
Eris - Plain. The big difference is that you need to get up into your special's blast radius, so you're more mobile, but it boosts all your damage by a big chunk, so it's really versatile with whatever normal builds you're into.
Hestia - Departure. Prioritizes huge first shots and frequent manual reloading; leans much more heavily on the attack-boosting boons (i.e. no Zeus/Dio/Ares) for those big multipliers. People like this one but I haven't gotten it to work for me personally.