Interestingly, I've just had a few experiments with stripping paint off a 1969 BSA Bantam. We do bead blasting where I work so that was the obvious first option. I dare say if your paying you'll get back a perfect bare metal frame, but in reality although bead blasting removes the paint, it also leaves a residue from the beads which needs to be cleaned off. This can be almost as bad as the paint! You'd be ok with a bike frame and forks but I also wouldn't use it on thin steel.
My second option was paint stripper, something like Nitromors. Again, it works but it takes quite a while, it also stinks and you'll need lots of steel wool to really remove all the paint. I did do a bike frame once like this and it took about 2 days and probably cost about £25 in stripper and steel wool.
Third option which I find the easiest and quickest is a wire brush on a drill. Screwfix sell a pack of three different types which will get into most awkward areas. Still best done outside because of the paint dust but you'll be left with a perfect bare steel frame and it leaves the surface with a nice key for the primer. I think a pack of 3 wire brushes is about £7 and you could do 3 or 4 frames, so its cheap as well