Don't worry about overspray, it'll be covered up by the overlying color.
As to color, black or dark grey is the norm. But you want to use anything that's going to conflict with the color of the plastic so you get a good contrast which will show through the final color. I've been messing around with several different browns and other colors just to see what happens. But then I'm an artist by nature, so I do silly stuff like that!
I've pre-shaded, cleaned the brush and then layed in the color right away with no problems. But, as with any painting, you'd probably best let it sit overnight or however long you usually like to let paint dry.
I have a different approach to pre-shading, myself. I just prime everything in black and build up the color; both the color of the paint scheme as well as any color variations which result from the effects of weathering, maintenance, etc. Some folks say that that's too hard or time consuming. I say they're just too lazy and impatient!
The true key to attempting anything like this is to get as much info on as many techniques as possible, mess around alot (maybe on a scrap model) and determine what works for you. You most likely will come up with a hybrid technique of your own which borrows from two or more other techniques. If anyone says "this is the ONLY way to do it", ignore 'em...
Fade to Black...