The thread title is deceiving. If a manual choke doesn't work as it should it's more operator error and not a choke issue. If it were a automatic choke the choke being out of adjustment will cause all sorts of issues.
Now it sounds like an overchoked situation with a misadjusted or misunderstood fast idle.
To the OP.
You should be able to press the throttle to the floor while pulling the choke out all the way.
Then as soon as it fires off push your choke back in just until the engines smooth's out but with a high idle. You MUST press the throttle while pulling the choke or the high idle will not set.
At this point it should be running smoothly around 1,500 RPM's
Once it starts warming up the idle will continue to climb, and at this point you should be able to take the choke off and tap the throttle to bring the idle down closer to normal.
I run and electric choke that is adjusted slightly on the lean side, as I would rather baby it a little at first than have it overchoke.
Point being, having to baby it a little by feathering the throttle for a minuet or two is preferable to a black smoke, rich as hell plug fouling condition.