billy has some good advise, a battery tender works great.
About the battery tray, mine too has been through the rusties. The tray comes out without too much trouble. I suggest to remove, take off the glides, sand, prime, and paint two coats with Rustoleum paint and rusty metal primer.
I fear undercoating products will be hard to get off if rust returns and you then decide to paint. I do like the rubber mat idea. I'll have to add that in mine.
If you are daring, buy a gallon of Muriatic acid from your local hardware or home improvement store. Handle with care in outdoor conditions as the fumes will get to you quickly. It will remove 100% of rust from steel FAST. The hard part will be finding a tray large enough to submerged the tray in. The acid can be diluted with water, 1/4 strength and works great. When the rust is gone, rinse with water, blow dry, then prime and paint.