So there are a few things there.
1. Please go along and do and introduction on the intro page....
https://www.airbrushforum.org/introductions/
2. Size of the needle/nozzle does not determine the size you work at, mostly...
3. Finer tips need skill and are best with experience as they can be finicky. They are more sensitive to reduction and pressure and learnign that only comes with time and practice.
4. There is no shortcut to getting skillful with the airbrush. I've seen guys paint on ridiculously small items with a 0.38mm eclipse...
5. Larger tips are needed for larger pigments. EG you can't practically spray primer through a 0.2mm nozzle...
So in answer to your questions... "Based on what size models I'll be working on, would the 0.2mm needle or 0.4mm needle be better?" Both and neither... depends what paint you are using, reduction, level of skill, level of detail needed, how much practice you are prepared to do.
Regarding the crown cap, is it particular to a needle/nozzle combination?
Now... here is a dragon to say Hi!
View attachment 60601