"Frank...
When was the last
"Frank...
When was the last time the motor had a tune up? Water separator, plugs, wires, cap & rotor. Clean the carb linkage well with spray carb cleaner. Shoot a bunch down the carb while its running to clean the plates and such. Start with that.
What you describe almost sounds like 2 different carb issues.
1)Opening the choke to get it to start means that it is too rich, not getting enough air. The choke is closed too tight. Does it have a choke pull-off (vacuum break) on the carb? This opens the choke plate a slight amount but has to be set to spec. for the engine to run properly right after/during start up. Spec may be very small -- 9/32" or so to let just a little air in there. When you open it manually, jam a screwdriver (or whatever)in it to keep the choke plate open, the mixture gets way too lean and you will get the backfire. The choke plate should be closed tight during the first couple seconds of cranking, but as soon as the engine fires up, vacuum will be made and the choke plate will crack open that small amount. If the engine cranks too long without starting (because of other problems, such as out of tune engine) you will run into flooding issues, fuel soak the plugs and have to jam that screwdriver down the carb. to start it.
2)The trying to accel out of a corner and having it quit sounds like its running too lean at that split second. It doesn't have any gas right then to get it to go. That sounds like the accelerator pump not squirting anything into the carb when you need it most. The throttle plate goes wide open and lets all that air in there, but the engine gets no gas to go.
You may not need a full rebuild on it. Thats alot of $$. You can probably get away with checking/adjusting/replacing that choke pull-off. They get a rip in the rubber diaphram inside and won't hold vacuum. The accel pump should be replacable as well. Check for other vacuum leaks as well, hoses coming off, dried and cracking, whatever.
Do that tune up.
Wrench"
