Fiberglass is one of the easiest mediums to work with, IMO. It is very forgiving, and simple tools and supplies are all you need. For what you are doing, I would suggest epoxy resin. It is more expensive than polyester, but it bites in better and is stronger. I usually use polyester, but to hold the weight of a battery you will need some strength there. Polyester would probably work, but you are only going to need a quart or so, therefore you won't be spending a whole lot more.
I would buy my supplies at a real boat supply place, not one of the so called discounters like West Marine or Boaters World. They get stupid money for their stuff. Look in the yellow pages for either a boatyard kind of place, or even a fiberglass supply house.
Buy mat, not cloth. It bites in better, and is easier to shape. Mat is the one that has random strands of glass running every which way, cloth is the woven stuff that has strands interwoven into a square pattern. About ounce and a half is heavy enough.
Also pick up a gallon of acetone for cleanup, some disposable brushes maybe an inch wide, stir sticks, plastic paint cups, and lots of latex gloves.
Start by wiping the area where you will be glassing down with acetone, really wet. You are removing the mold release wax.......do it several times. Then take a body grinder and roughen up the area where you will be glassing. This gives it tooth for the new glass to bond to. Then wipe it down again with acetone. You are now ready to start glassing.
Mix up your resin in about 12 oz batches, it will kick in about 15 minutes after you add the correct amount of hardner, so you will waste some if you mix up too much. Start by painting a good coat of catalyzed resin onto the area where you will be glassing. Oh, I forgot, have all of your mat precut into strips ready to go........make some 2 inches wide, some 3, and some 4 inches wide, maybe 6 inches long.
Lay down some of the 2 inch mat into the resin you painted, and then start dabbing the brush with more resin into it until it is wet and translucent. Keep doing that as you lay up more of the 2 inch strips. Then start putting the 3 inch ones on top of the 2 inch ones, overlapping them. The idea is to progressively keep putting bigger pieces to spread out the load. Finally, lay on the 4 inch wide pieces and dab a coat of resin on top of that.
The reason you dab instead of brush is that brushing pulls the mat, but dabbing just makes it wet. Obviously, this is a simplistic description of how to do glassing, but it is easy to get the hang of it, and once you do it you will understand how easy it is to work with.
Good luck.
Don