Depending on how recently the projector has been in regular use, it may not need any actual restoration to show films--only basic maintenance, oiling, etc., after an inspection for worn parts. If you want to show movies at home, you may want to adapt a carbon arc lamphouse to use a tungsten-halogen lamp. You'll also need to find something to use as a preamp to take the audio feed from the sound reader before going through your home stereo system. If the sound head has got a red LED reader, you'll probably want to convert it back to an old exciter lamp setup for older prints that don't have cyan soundtracks. You'll be better off with a solar cell (a Dolby split cell would be best) instead of a photoelectric cell, unless you're into servicing antique electronics and can find spare parts. Since most theatres trashed their optical sound systems for LEDs a few years back, you may find some still around for free.
If the projector hasn't actually been used since the silent era, it will not have a sound head, and will be a more likely candidate for "restoration" to make it look and operate the way it did in the 1920s. In that case it will surely need a thorough cleaning, new oil, and quite probably some new/rebuilt/spare parts. Some gears and rollers may be locked tight and may need to be disassembled and/or replaced. You will then probably want to keep the carbon lamphouse intact but may have a chore making it operable without updating it at least somewhat. You can also try rigging up a new tungsten lamp and reflector inside the existing lamphouse so you can use it while keeping its outside appearance intact. A really early projector will have no reflector inside the lamphouse.
Keep us posted on your progress! Even though it's noisy and inconvenient, projecting 35mm film at home is a much more satisfying experience than popping in a DVD or BluRay disc fed into an LCD projector.
--Christopher Jacobs
(who's done both, but unfortunately has to settle for video or 16mm at home these days)
http://www.und.edu/instruct/cjacobs
http://hpr1.com/film/archive/