Welcome to the forum, Arlin, and thank you for serving! Maybe we can get you interested in building models, too?
As far as an airbrush goes, I'm sure there'll be almost as many suggestions as there are guys who use them.
For myself, I have a Paasche VL, double-action, siphon-fed airbrush, which I power with a Craftsman 1.5 hp, 3-gallon compressor and tank. I am just learning how to spray with minimal overspray, and to paint fine lines. I'm learning to use very low pressure, to start with. And in my case, building airplanes and other subjects of a size somewhat larger than a lure, I can also use masking, using putty, for example, to help reduce overspray.
I use the the Craftsman compressor, because I have other Craftsman air tools, but it's not absolutely necessary. There are inexpensive brands available, such as from Harbor Freight. And there are guys who use cans of compressed air, or who use a gas bottle and have it filled at intervals.
But if I were to paint a fishing lure, I think I'd tend to lay down the base colors with an airbrush or a rattle can, and then paint the finer details by hand.
Anyway, I hope that helps give some insight, and I'm sure the others will be happy to offer their experience, too.
Again, welcome, and do show us your work!
Best regards.
Brad