Hi Buckets,
that looks to be a Ryan half crank engine as used in Ryobi whipper snippers for years.
One question you could ask is how long since last use.
The carby diaphrams can get hard after a long time of non use which means a kit is required.
Check the basics like spark, filter and fuel lines first, before looking at the carby.
As for the choke, A is full choke (closed intake), B partial choke (partially closed intake in diagram) and the far right is engine running position -fully open air intake.
Does this have a primer bulb? If not you fully depress throttle and pull the starter with choke in position A until you hear a pop of the engine, move to B and it should start right up with the throttle in idle, wait a few seconds then move to C run position.
