Your stain can either be wiped or sprayed on, your prefernce. If you get dyes they can be mixed into most clears and then sprayed on.
As for applying your clear coats, oil finishes are the easiest to apply since you just wipe them on and then the excess off. Any of the lacquers or urethanes need to be sprayed on, brushing won't cut it. A spray gun and air compressor that can handle the gun is going to spray the best. I would say at least a 30 gallon air compressor is minimum. Airbrushes will work for bursting and can get you by for color coats, but fall way short for spraying the clears. A lot of stores are selling Preval sprayers which is a glass jar and a can of propellant that lets you mix your own fluids and spray as you like. I've used them and don't like the spray pattern, and had a tough time getting good atomization. I would say you are better using rattle cans of nitro lacquer. I personally like the Reranch brand nitro or Deft nitro. You can check some autobody suppliers in your area, some of them will fill spray cans with 2-part urethanes and colors as well.