hesatation out of the hole

I'd say the fuel filter would be the first thing to change. It can get a lot more complicated than just that and sounds like a general tune-up would get you back in shape.

With a new purchase, a tune-up is in order. Probably the last thing the Seller will do is the little $40 jobs.

both are correct, but what i find as an item that is often over looked is the flame arrestor. clean it. ( misaligned belt driven items will clog it up with belt dust.)

do the tune up, change both the fuel filters ( dirty filters are more of a fuel starvation at higher engine speeds.)

be extra carefull with the accelerator pump diaphram. those small screws are easily stripped if they have been overtightened into the pot metal. there is a small check valve on the housing that maybe clogged or letting the fuel backwash into the bowl. clean that. there is also an orfice on the metering plate that may also be gummed up being low in the fuel bowl.

there is also a vac orfice that goes into the choke housing that may be leaking.

the fuel in the primary well needs to aireate. if it's not, it will cause a sluggish response.

timing, dwell, mixture and the idle setting are all inter-related. set the dwell first. make it idle at 600 to set the time. SOME carbs just close the primary plate at idle. SOME are set with a feeler or wire. (book time) last but not least you set the mixture.

don't do it in any other order or you will get bad off idle response.

I agree with dan, most hesitation in any motor is usually caused from improper valve, ignition timing. I would adavnce the ignition timing, before advancing to the parts changing step. It will diagnose your motor for you, provided everything else is copisetic, and you have no vacuum leaks.