Depends.
Here in MI, summer is short, so if i'm planning on sanding/restenciling a cabinet or spraying a playfield (anything outside, basically), it may get dictated by season. If I bought a game today, I'd start on the cosmetics first. If I got it in January, cleaning and electronics in the basement.
In most cases I'll usually spend a week or so doing some basic cleaning, fix easy/obvious stuff, and playing it...