Hi, L. The "brass" fireplace screen is probably just brass plated. You can check for sure by scratching a spot in the back that is out of sight. You will probably see a grey metallic shine at the base of the scratch rather than a bright yellow that would meant that it was real brass. If it is real brass, I certainly would not paint it. You should be able to sell it for enough to buy a new steel one.
If it is steel, you can sand with about 320 grit emery paper (wet or dry--the grey stuff) to roughen up the surface so the new paint will stick. Wipe it down or brush it off to get rid of all the sanding dust.
Certainly, the easiest and best way to paint would be to spray it. You might want to look at the high temperature paints in spray cans at the auto supply store or mass marketer. You will not have a great color choice, and you really do not need the high temp paint, but it would offer a little protection if you can find a color that you like. Be careful of overspray and put newspapers down WAY around where you will be spraying.