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Now should I have the user info in one table and the character info in another or should they both be in the same table?
Keep an eye towards flexibility when you design your data. A user is a user and a character is a character. In a "future version," maybe you'll want multiple characters per player, characters with no player, etc. Right now you want to ensure a one-to-one correspondence between player and character. That's all possible with 2 tables.