Lots of ways to do the repair. Only one way to do it completely right which would be to remove and have it media blasted. Now having said that, I would not go to that extent. I am a big fan of the rust reformer type products as mentioned before. The best one I personally have found is sold at NAPA. I believe made by Permatex. Seems to do a much better job than others I have used.
On painting it. I have good luck with Rustoleum with a foam brush or roller. If you are careful you can get it applied and it will level out as it dries. I also am a big advocate of mixing the Rustoleum with a "catalyst" or hardener. Although not normally seen at Lowes or HD. I buy it at Tractor Supply. It really make the paint last longer and fade resistant. Also makes it more fuel and solvent resistant. Just remember that what you mix will only last a short time so don't mix more than you will need or you will end up with a lot wasted.