When to paint?

What are you building? Aircraft, Armor, Autos, Ships, Sci-Fi, etc. Probably get better answers with more specific Questions. Personally, I don't paint any parts on the trees as you have to then touch them up after removal, but many modelers do.

I'm interested in Sci Fi and WWII warbirds. Right now though, I am working on a F-15C.

QUOTE: I'm figuring it out by trial and error

That's pretty much the way to go.
It all depends on what you're building, and what you think will be easier for you. For airplanes, I tend to paint all the landing gear separately. Tanks and AFV's get their wheel assemblies all painted separately, then added to the model. I see some people building the whole thing then painting it. I have NO CLUE how this would be done, so a lot of my subassemblies are painted separately.
Pretty much, take a look at the instructions. Anything that might be hard to get to when on the model is a good thing to paint while off the model

I agree with rjkplasticmod in that I never paint anything on the sprue. I airbrush everything that I can, so everything is usually trimmed and sanded by the time it gets painted. Small parts are easier to hold onto if left on the sprue, but when I try that by the time I've cut them off and trimmed them and sanded them most of what I painted is gone anyway!

As zokissima said, there is no perfect way to know how to know what to paint before assembly. I also try to do "Subassemblies" when I can. If I can clue some parts together and paint them at one time, I can fill any gaps or make any minor adjustments before they are painted. The paint also helps fill minor gaps in the assembly. On the other side of the coin, a complicated assembly can be difficult to paint evenly. You are doing it the right way, trial and error and learn as you go. There are no clear-cut rules.

On your F-15, for example. If you build the engine before painting it is going to be virtually impossible to paint the inside of it evenly. On the other hand, assembling it and filling the gaps before painting the outside would be the way to go, IMO. I'd probably spray the inside, assemble it, fill any gaps, plug the ends, and spray the outside. In fact that is the way I did the engine on my F-105 .

With tanks, I have been learning to paint first and then assemble.

When I build a plane or jet, I will tend to hand paint the interior, and airbrush the outside.

Some parts are not a big deal to paint on the sprue first, unless you are one of the detail nuts in which case the the parts are painted off the sprue.