I have some cheap-brand superglue and it works fine. Krazy Glue, if you want to go with a brand, but really, any will do. Just be careful about excess glue squeezing out, so only put enough on the piece to hold it together. Else, a cotton swab and a bit of nail polish remover will take off the excess, but be really, really careful, because it will take off paint.
As for stubborn shoulder joints, if the figure is in a warm room, try rotating the joint to work it loose. Regular wear and tear will loosen joints nicely. My D-Arts Mewtwo has a stubborn shoulder joint, and the most I've done was warm it with my hands and rotate it slowly to work it into position, followed by rotating the joint to loosen it. Make sure to hold the joint itself, don't rotate below the bicep swivel. Holding the joint will also help warm it.