For getting into lugjoints and braze-ons, it is nice to have a brass brisle brush in a Dremel tool. If it is a steel frame, then you can get away with a more effective steel brush. For a lot of steel frames, I go one bigger and use a 4 inch rotary brush in an angle grinder. Average strip time, 30 mins.
I have used a frame size sandblaster before on frames, and for the most part I like the brush better. The thing with a sandblaster is it can very easily cause sand to get inside the tubes where it is a challenge to remove.
Chem stripper is good if you have a particularly stubborn finish or no access to any of the afore mentioned tools. You will still need a small brass brush for working it into said areas. Be totaly certain to neutralize and remove all of your remover before adding primers, as it can cause metal corrosion if left in place for extended periods(the process should only take one session).