HIGHLY recommend Hunter X Hunter
One Piece is amazing, but the odd art style can put people off at first
those are the big shounen series I would recommend...
you might also consider My Hero Academia, but there arte only like 8 or so episodes out right now, new episodes come out on Sunday night/monday morning
getting away from shounen stuff
Erased was amazing last season, if you haven't seen attack on Titan, you should
Gate is really good
you might dig terraformars it is like starship troopers meets dbz, huge buff men fighting giant humanoid cockroaches on Mars.... and then mena re augmented with abilities from various animals and insects
have you watched any of the JoJo series?
there is just more than I can possibly name... every 3 months like 40 new shows come out, of those about 10-20 are good, and from there you need to hone in our specific interests
the ebst palce for anime btw is Crunchyroll... consider a trial membership (free), but even after that expires you can still watch stuff, just a week behind other users, with commercials, and in SD
if you get crunchyroll, or try the trial... my favorite current anime series is re zero, but you might also consider big order, twin star exorcists, bungo stray dogs, and cerberus
the thing with anime is that there is LOADS of it, and it covers basically every genre imaginable... murder mystery, highschool life, action, horror, science fiction, fantasy... and every combination there in.... so it is hard to simply say "watch this anime" it is easier to ask what kind of experience you want (not limited to anime)... like "I want epic fantasy".. or "I want something really sad"