The Prima Guide says Aquaman is a good beginner character and that Joker is not a beginner character.
As a relative beginner myself I'd recommend:
1) Play someone you like. If you hate Aquaman, don't play Aquaman. You aren't going to want to practice much if your character doesn't inspire you. Whoever you pick, you'll be spending hours and days in the lab practicing with, so it should be someone you are passionate about. I hate zombies, so I'm never going to play Grundy. Even if Grundy was objectively a good starting character, he isn't for me.
2) Play someone who fits your style. For example, Doomsday is a relatively good starting character, but he is all about aggressively charging in and laying the smack down on his opponents. If you aren't about the rushdown, then Doomsday wouldn't be your character. If you want projectiles, then that eliminates a few characters. At the same time, if you hate projectiles, then you don't want a zoning character. I like to have some projectiles, so that eliminated Catwoman, Flash, Doomsday, and a few others for me.
3) Play a character with a minimum of Special Moves. It is better to have a character that does a few things well instead of a dozen things that you can't do well. For example, Raven is probably not a good starter character. She has a bunch of moves and then when she activates her trait she has a bunch more moves. That's a lot of stuff to try to master, IMHO.
4) Avoid low tier. Winning isn't everything, but yes it is. At the very least, losing sucks and is discouraging. If you are a high level player who thinks a character is underrated and you want to be its champion, that is one thing. As a beginner though, why handicap yourself by trying to buck the tide and play a character that has too many bad match-ups or flaws?
5) Play a character that some top players main. It is good to have a model, a "hero" player, someone to try to aspire to play like. I'm a firm believer in that approach. Some characters like Hawkgirl, Lobo, and Cyborg haven't been getting a lot of play in tournaments, so it is hard to find examples of high level play. Other characters have a lot of examples. If you like Aquaman you can watch how Tom Brady, Dizzy, and others do it; if you like Superman you can watch CD Jr, KDZ, and others; and so on.