thats a nice clean 650sx, good buy. It looks like you do have a small carb.
Changing out to a bigger carb is pretty easy. What you would need to change out the carb to a 44 sbn(which has been stated before) is a adapter plate (or if you find a intake manifold, those are even better), the 44 sbn carb itself, gaskets, and possibly even an air filter. The nice thing about the stock carb that you have is the air filter itself does a pretty good job of keeping water out. The big difference that a larger carb would bring to the table is Throttle response. Which is always fun.
You have a nice exhaust pipe for sure, and the grate that is on your ski does wonders for hooking up on the water. You might want to buy a primer kit.
For now with what you have, I would just say get out and ride. Have a blast, if your ever down in Knoxville, TN. Let me know, I'll ride with ya. And welcome to your new addiction