What is the best RPM for shifting gears?
That would depend on the engine, car and driving conditions. A small engine might need to be shifted at 5,000 rpm or higher when merging onto the freeway but in normal driving 3,000 rpm might be just fine.
It doesn't hurt to wind it out a little but you don't want to go nuts . The car will let you know
If you don't have a feel for when to shift you should probably drive an automatic.