You should definitely check out 'Ultimate Spider-Man'. It reimagines the origin story and has a modern touch. Another one is 'Spider-Man: Noir', which gives a darker and more gritty take on the character.
I'd recommend 'The Amazing Spider-Man' series. It's a classic and has some great storylines and character development.
Well, 'Spider-Man: Miles Morales' is a good choice if you're looking for a fresh take. It focuses on a new hero with ties to the Spider-Man universe and offers a unique perspective. Also, 'Spider-Verse' is quite exciting, with multiple versions of Spider-Man coming together.