First- - - -make sure the choke cable moves freely, and the choke plate closes fully when the knob is pulled.
Cold start: Pull the choke knob all the way out, make sure the ignition switch is "on", and crank the engine until it fires. A well tuned engine with a hot battery shouldn't have to be cranked for over 5 seconds, even if it hasn't been started for a while. As soon as the engine hits, push the choke knob in halfway. The engine SHOULD run at fast idle without any attention to the throttle at all. After half a minute or so of warmup, you should be able to push the choke knob in fully and the engine should "slow-idle" normally. If the engine refuses to start and warm up with the above procedure, you have either carburetor and/or ignition problems, of possibly a vacuum leak somewhere. Hot starts should not require ANY choking. If a hot engine sits for a few minutes and is difficult to start, it's probably flooded. Hold the throttle wide open- - - -no choke, and crank until it starts.
I suspect you've got bad starter connections, dirty points, or internal carburetor problems. Most "carburetor" troubles are actually electrical- - - - -at least during the 65+ years I made a living as a mechanic, shop owner, and shop teacher. Now I'm just an opinionated old geezer who likes to stir the pot on internet forums!
Jerry