You can probably get a better finish with them removed and it would be easier if you were planning to use spray paint. However, I can almost guarantee that you will scratch some of the paint on the front ones when refitting the spring clip.
I've always brush painted mine in situe as some brush marks are hardly going to be seen behind a wheel.
The cleaner you can get them, the better the paint will last, so get some nitrile gloves (tend to be much better than latex) a couple of cans of brake cleaner, a stiff wire brush for the flat accessible areas, a fine wire brush for getting into the tighter parts and go mental.
Unless you can do them all quickly in one swift hit, get four cheap 1/2 inch and 1 inch brushes means you could do one caliper at a time as the paint dries fairly quick.
As said, just keep off the disc surface or clean off any mishaps before driving.