What is the desired effect here? Is this just for fun and the end result doesn't really matter or are you trying for something that's going to impress people? If the former, wash the wheel to remove any traces of oil on the parts, let it dry really well (use a hair dryer if impatient) and go to town with some spray paint. As FB suggested, there's not much that you'll get paint on that will really matter. It will quickly be removed by your brake pads or chain, in the case of the cassette/freewheel.

Now, if you want to impress people, the only way you are going to do a satisfactory job is to disassemble the entire wheel, carefully prepare the various metal surfaces, carefully mask the brake track, and use something better than Krylon. Ideally, you'd be powder coating or anodizing the aluminum bits (depends on the look you want) and eletrocoating or PVD'ing the spokes (assuming you want something other than black). This will cost you a bunch of time and money of course, but will yield very nice results that you can be proud of.