I've read some half correct, and therefore half incorrect, responses. Here's the deal:
If the carb is working properly, and it probably isn't, more on that below, on a cold engine, you cycle the gas pedal ONCE, to set the choke. All the way to the floor and all the way back up. Then open the throttle part way and crank. Be patient. If you haven't driven it in a while, it might take up to 10 seconds to start (if the fuel pump is in good shape). No extra pumping! Don't move your foot. Be patient. The movement of air past the venturi will draw fuel from the carb into the intake manifold. You do not need to use the accelerator pump. The engine will start and run at fast idle. Let it run there for 2 minutes or so, then stab the gas pedal and see if it starts to kick down. Alternatively, if everything is properly adjusted, you can drive immediately.
In your Example 1, you said that the engine started fine after you got home, which was after you had cranked it earlier. It started fine because you filled the bowl when you cranked it earlier. Earlier, when it sputtered, the choke probably wasn't set.
In Example 2, first sentence, you experienced the same situation as when you returned from practice. The bowl was full so it started quickly. In the second sentence of #2, it sputtered because you didn't reset the choke and the engine cooled off a bit. In the third sentence of Example 2, it stalls and dies because you didn't warm it up all the way, AND the choke pulls off too soon because it's old and the spring has weakened. It's also likely that the seal on the accelerator pump is old and stiff, which will cause a bog that can stall the engine.
Things to do:
1. Make sure you have fresh gas.
2. Use the proper starting sequence that I mentioned above.
3. Tighten up on the choke spring a very little bit at a time. Start the engine when it's dead cold and drive it immediately. Cold drivability should improve. If it's better but still not right, let it fully cool. like overnight, and repeat. It will never be the same as when it is warmed up like an FI engine is, but it should be totally drivable and reasonably smooth when cold, just a bit down on power.
4. If #2 works, but you still have a bog when accelerating from a stop, get a new accelerator pump. They're cheap and not too hard to replace.
5. If you experience hard starting and bad idling on a fully warm engine that has sat for a short period, like 10 minutes, that's probably a little bit of vapor lock. Start it again and run it at higher RPM for a few seconds until it runs smooth, than let it idle.
If it runs fine on non-ethanol gas, and it probably does because that is what it is likely calibrated for, there's a good chance it will run like crap on gas with ethanol. Be ready for that if you go someplace where you can't find non-ethanol gas. Be ready to richen the idle circuit by turning the idle mixture screws until it runs better.
Source for all the above: I've had a bunch of GM cars with carbs and have been relearning all of this over the past 3 years with my '77 Grand Prix. Even after doing all the above, it still idled just a tiny bit rough. And then I drove it some more and it's perfect now. Engines need to be used. Try do drive the Jeep every 2 weeks or so, long enough to fully warn it up.
