I've been in exactly your position.
My advice is not to bowl, at least not for a couple of weeks. If you've got a doctor giving you an 8-week estimation on full health, however, two weeks might not nearly be enough.
Using a properly fitting wrist brace will help when you decide to return, but only if you already know how to use one. I bowl with one or without one depending on how my wrist feels. It's almost two completely different styles of bowling and having the brace on won't equal automatic protection for your wrist. Even when I wear a brace I am capable of overexerting my wrist. If you're just learning how to throw with a brace, it may take some time to get accustomed to it, which could foul up your A-game not to mention making you a liability for your team.
As to which brace to use, it's hard to say. I've found the adjustable braces are the way to go, because a straight-back brace might not offer your wrist support in the place it needs it most. I have to use one that holds my wrist in a slight cup due to where my injury is.
Jess