RE: Nexstar Engine Issues
When you say that you have it adjusted at the leanest setting, are you referring to the high-speed adjustment (the needle valve), or the low speed adjustment (the screw in the center of the throttle arm)?
Your symptoms indicate over-rich low speed mixture. Usually the low speed needle factory setting is initially too rich, but the engine improves somewhat with run time & it is generally usefull to get some run time on it before messing with low speed settings.
As soon as you get it started, smoothly advance the throttle with the glo-starter still attached -- this should help get it up to speed without drowning. When it is running at full throttle, remove the glo-starter & set the high-speed adjustment so that the engine is developing very close to max power. If the factory NV limiter settings are correct, you should be able to run the engine at full lean on the NV without fear of damage.
Just in case they aren't set properly, when adjusting the HS needle, keep leaning it until the engine peaks -- try to go past the peak & see if it starts to slow down. If it does, quickly back off the needle and approach the peak again from the rich side. When fully peaked without slowing, richen the mixture until the engine begins to slow slightly & leave it there.
After a few full throttle runs you can set the low speed needle.
Shut down the engine & adjust the low speed setting by turning the screw-head, inside the hole in the center of the throttle arm, clockwise 1/8 turn.
Restart & try it out. Keep adjusting the low-speed setting in 1/8 turn increments until the engine will hold a steady idle & then accelerate smoothly from a prolonged idle.
If you get the low speed needle too lean, the engine will die away at part throttle, or quit sharply (no sagging or sputtering) when you try to accelerate from idle, or even refuse to start, or just run a few seconds and die.
If you aren't getting anywhere, ask one of your instructors to help you.