dont' worry about carburetors ... they cost less than $100. so you should be ok if there is anything wrong.
what you want a moped to have at minimum is:
- non-seized engine (but depending on how it's seized, you can easily fix that)
- a good cylinder (these are expensive to replace, whereas rings/piston are not)
- decent carburetor
- working clutch on engine
- good magneto/coil, etc.
everything else is secondary. you can get headlights and tailights later. side panels and other aesthetic parts. no chain on the moped? order one (they're not expensive). no tires (or flat ones)? ditto on replacement.
what you don't want is a pretty looking moped that has a shit engine on it. engines are hard to come by and expensive.