I am currently in the process of refinishing an SG. I used sandpaper to strip the paint because I was too cheap to buy the chemicals. Be careful though, its easy to sand into the wood and create valleys. Yes, be careful on the neck. For this part, I put the power sander away and sanded by hand. It took a long time, but its easier to follow the contours of the neck. Yes, use primer before you paint, it gives the paint an even surface to cling to.
Hope this helps