Hi, GK. As is usual with most painting projects, surface prep is the key to a good job. I would wash the piece with Tri-Sodium Phosphate (TSP) available at any home center, then sand with 100 grit. Next I would wipe it down with acetone as long as you have good ventilation and can get away from sources of ignition. If this is impossible, then vacuum the surface and tack rag.
If you are pretty sure that the old paint is enamel, I would stick with that and spray cans work fine for most projects. I don't know what color you are looking for but don't forget that they also sell paint in auto parts stores. Dupli-Color has a line of enamel and also a general purpose line, both available in many colors if you can't find what you are seeking in a home center. If you are not making a great color change, then you can probably get by without a primer. The surface should also be in very good shape if you want to to this way. If both of these conditions aren't met, then go with a primer that is from the same manufacturer and brand as the paint and as close to your color choice as possible. After you prime, sand with 150 grit, vacuum the surface and tack rag. Then you are ready to spray.
It's sometimes difficult to cover all the bases with limited info but this should not be too far wrong. Before you commit to spraying the whole thing, I would test spray a small area in an unobtrusive spot and wait the recommended time for drying to be sure that everything was compatible. I would also try to get the highest priced paint that you can find. This is not a perfect indicator of quality, but it's about the best available. Little things like a good nozzle on the paint spray can will make a lot of difference in the project. Cheap spray cans usually come with cheap nozzles. With any of the chemicals including the paint, be sure to read and follow the manufacturers directions.
Good luck and hope the bed comes out great. Henry in MI