Weapons are your main mode of attack. Initially, only the Stygian Blade is available, but additional weapons can be unlocked by spending Chthonic Keys in the Arsenal Room. Unlocking all the weapons requires a total of 24 Chthonic Keys. They can be upgraded during a run with a Daedalus Hammer.
hades.fandom.com
I personally liked the shield the most. Close quarter combat against everyone but the bosses, whom I liked to throw the shield against.
Also, the things you get during your escape runs are very important to the playstyle. I eventually got a strategy down that I was able to replicate with pretty much every run.
Duo boons are super useful. I particularly liked getting Stubborn Roots and Merciful End, though others are good as well. I'd start every run with the Athena keepsake and get Divine Dash right off the bat because of its blocking ability. I also really liked getting Crystal Beam (Demeiter) because it's another long-range damage attack (used as a cast) that's really useful especially against bosses.