I'd use paint thiner instead of alcohol to wipe down after stripping. The thinner will remove residue better than the alcohol, and has a longer open time. It will also highlight the areas in which there is still some leftover stain or finish.
If old finish isn't removed, those areas will have a different color than areas with no finish, once the stain is applied.
Sanding helps 1) remove thin layers of leftover finish or stain, 2) removes any "hairs" or raised grain, and 3) preps the surface and opens wood pores to cause better stain absorption or finish adhesion.
Bob "Boardman" Borders