Mikuni is a Japanese brand of performance carburetors. Mikuni's range of carbs is quite large, but there are few types and sizes that are very suitable for pairing with a large bore cylinder kit on your moped. Historically they've been popular for use on scooters and small motorcycles, but with the availability of appropriate intake manifolds, they're proving great for mopeds too.
Mikuni carbs' main jets are extremely easy to change, and are also known for being much easier to tune correctly than the Dellorto PHBG. However, their larger sizes often require throttle modification or a new throttle that has a bigger range of motion; their size also makes them difficult to mount on certain mopeds.
VM series (round slide)
The VM series is the more popular type of Mikuni carb to use on mopeds, and come in sizes ranging from 16mm to 44mm. By far the most popular model is the 20mm VM20-273, or simply VM20. Other popular sizes are the VM22, VM26 (if you're going to get a little crazy) and VM28 (crazier still).
There are several different flange mount intakes available to use the VM20 and VM22 on Tomos kits, Puch reed kits, Puch Gilardoni kits, and the Honda MB5. It's very tricky to mount these carbs on Peugeot and Motobecane engines.
TM series (flat slide)
The TM series are not nearly as popular as the VM series. They are generally just as suitable for use on two-strokes, but are commonly believed to be better for four stroke engines since they come tuned for four strokes out of the box. They range from 24mm to 40mm in size, but of course, the TM24 and TM28 are really the only sizes you'll want to consider.