I forgot to address the equipment part of your question. I would advise ditching the T862++ unless you don't plan to work on anything bigger than a cell phone or tablet--the preheater is too small and it's almost impossible to produce a smooth heating profile. There are some good BGA rework stations for under $1000. See the forums for a wide range of experience with and recommendations for each. If you want to keep it ultra cheap, get a T-8280 pre-heater and a hot air station that has even heat distribution. I have a W.E.P. and it's very good in that regard. Avoid anything by Aoyue.
You will also need appropriate flux, a reballing jig, a variety of solder ball sizes and BGA stencils, tweezers, suction pen, temperature meter with 2 thermocouples, lead-free capable soldering station (Hakko or JBC), leaded solder, solvent (IPA, acetone and possibly MEK) and dispensers, lint-free wipes/gauze pads, lighted magnifier, lots of trashed boards to practice on and lots of patience to cope with the frustration of trying to develop profiles for your equipment and environment. Also really important is a ventilation system to draw away the fumes from the flux, which is quite toxic, and possibly a respirator. If I think of anything I've left out, I'll add it later. Have fun!
Edit: You can also try a Presto griddle as a pre-heater instead of the T-8280, but it will be difficult to get temps high enough and stable enough to be a good alternative to the T-8280. See the excellent articles by "dream" in the first link I provided for how to get professional results on the cheap. You will also need a variety of nozzle sizes for the hot air station, and a fan to cool things down after lifting/attaching the BGA. And high temp aluminum tape and Kapton tape, and solder wick.
