Mosey,

You can do it and I bet you will have a great since of accomplishment in the end.

A couple of tips;
1) do you have a spare shower in case this one takes longer than expected? If not start on a friday night not sunday.
2) Since the back of the shower is in the closet cut an access whole if one does not already exist. You can make a cover out of plywood and modling or buy a plastic cover.
3) Check the instructions. On some of these valves you need to be very carefull about sweating fitting to them. They are often 1/2 NPT threaded and so you don't sweat directly to the vavle. In fact you may be able to unscrew the existing vavle and screw in the new. Unlikely but check it out first.
4) Definately try the copper sweating out in the shop first. The key is that the solder sticks to copper but not copper oxide. The cleaning and flux remove the oxide prior to solder melting and forming the bond. The copper should shine and you should be willing to eat off it (prior to the flux applicatioin!!!). I like the wire brushes better than emory cloth since the cloth leaves a lot of residue.
5) Carefull with that torch. You can set things on fire in a hurry.
6) Pressure test the final product with compressed air prior to water. I plumbed up my whole house with copper and pressure tested it prior to use with an air compressor. It very easy just get a pressure gauge, schreider valve, and two valaves. I put the schreider vavle into a 1/2 NPT ball valve and then a 1/2 NPT T. The pressure gauge goes in one end of the T and the two ball valves go opposite each other in the other arms of the T. Now you connect the open vavle end to the water system. This is a neat setup since you can use a air compressor to add air through the schreider valve and monitor any leak down with the pressure gauge. If it will hold 100 psi for 12 hours you know that you have no leaks. Be careful and make sure that the tub faucet and anything else on the water line can handle the 100 psi!!!! If not then use what ever lower pressure the whole system can stand.
I will try to get a picture of the setup I made.

Hope this helps.

If you can show us a picture maybe we can walk you through it.

Fred