Early versions of WearComp used lead-acid batteries. Later (Mid '80s) versions used NiCad batteries.
Lead-acid batteries are typically available surplus (e.g. taken out of used surplus equipment or the like) for around $10 each. For constant operation you will want to obtain at least two 12 volt batteries. These batteries typically have lugs that connect to crimp-on connectors. However, in wearable applications, the lugs are easily broken off or shorted (fire/explosion hazard) by stray materials such as keys or tools one might be carrying in a pocket with the batteries. Therefore, I generally soldered wires right to the lugs, and then insulated these very well.
Be sure to place a fuse right next to one of the lugs of the battery, not in the cord going to the battery. The reason for this is that if the fuse is in the cord, something can wear through the insulation on the cord upstream of the fuse, and cause a fire/explosion or the like.
The best fuses to use are the automotive type that have solder lugs. Place a fuse right near the positive lug, as close as possible. Typically one lug of the fuse can be soldered right to the positive lug of the battery. Now solder a red wire to the other end of the fuse, and solder a black wire to the negative lug of the battery. Wrap both lugs in several layers of fiberglass tape and epoxy. It is important to totally encase both the positive lug, and the fuse near it, wrapping all the way around the entire battery for strength, as general wear and tear on wearable apparatus is much higher than for other uses.