I recently purchased an antique Singer sewing machine. I'm guessing from around 1910's. It is in pretty good shape but needs to be sanded and stained. Don't know the first thing about this and would like to do it myself. Should I sand it or would it be best to just strip it? As for varnish, Should I use it or a stain? Help, Please...

First decide if you want to do this for your own satisfaction or do you want to retain any possible value as an antique, because refinishing antiques lowers their value. Some Singer models are more valuable than others, so I'd check into that first.
Before refinishing it helps to know what the wood is (possibly maple or birch if light beige and not grainy, oak if more yellow or reddish with little straight dark flecks), and whether is was varnished or shellacked, and whether stained underneath or just darkened with age. It's not vital info but good to have, especially if you leave the legs as is and want it all to match.
Stripping with chemicals is tough on any wood and any grainy wood like oak tends to leave stuff in the grains which are slightly indented. You could buy the smallest can and a scraper and do the worst parts with it. Or just sand. A belt sander if used properly so that no gouge marks are left is fastest, then more sanding with a palm sander or by hand, with finer and finer grits. You could start with 40 and end with 180 or even higher. Then wipe down with mineral spirits and maybe use a polyurethane that has a stain in it, or a stain/synthetic oil combination such as Minwax sells. Or a separate stain and cover coat. Your choice. I'd use the Minwax combination because it's fast and even and comes in many colors.

I would use Formby's Furniture Refinisher and Tung Oil on it.
http://www.formbys.com/products/refinisher.cfm
I have done this to 1940's furniture to restore the original look.