Google semi tubular rivets to find many suppliers of rivets and tools.
To determine length, see this chart:
http://www.rivetsinstock.com/rivets/semitubular-rivets.htmlFor example, for 1/8" dia semi tubular rivets, length = grip + 0.075", where grip is the material thickness to be riveted.
If you have access to both sides of the rivet, you can save on tooling by using a hand clincher, hammer, and a buck. An example of a buck would be a 1/4"-3/8" dia steel rod held in a rigid vice with the head of the rivet placed on the tip of the rod. The rod tip should be dished to the shape of the rivet head.
See hand clinchers here. What is called the "optional squeezer die" is how the dished end of the rod above should be made, or you could buy their die and stick it in the drilled end of a rod or other fixture.
http://www.hansonrivet.com/hand-rivet-clinchers.htm As said at this site, you can squeeze in a drill press if you have room. The clincher would be held in the drill press chuck, and the squeezer die would be held below. This gives an idea of how much force is needed to squeeze a rivet. Hint: don't turn the power on.
Photo is a clincher I made on my lathe.