No brush! You're better off spray painting. Spray painting and air brushing throw down an even layer of paint pigment that uniformly settles on the painted surface. It looks smooth. Brush painting flattens out the pigment and the result is nowhere near as smooth and can, oftentimes, look very mottled and inconsistent. If you're going for a near-chrome look, do NOT use a paint brush.
There are two schools of thought on the time when to paint. I usually paint the parts ahead of time, followed by assembly and touch-up as needed afterwards. Others like to paint once the model is built, but that can sometime add extra effort in the masking of windows and other openings. This can be particularly troublesome if you intend to light the model, like I normally do (hence, painting before assembly). In your case, however, since you plan on painting everything one uniform color, without decals (and I'm assuming without lighting), I would advise painting after assembly.