Apart from the better film festivals, most are shown on video nowadays.
If you go the video route, you’ll need a video projector and a video (as well as an exhibition license if the film is still under copyright or your video has copyrighted special content on it, like replaced intertitles, reconstructed sequences, etc.). Get a nice CRT projector, LCD looks like crap when blown-up to 30ft.
If you go for real film, you’ll need a couple of projectors, either 16mm or 35mm, depending on your budget and what format you can find the film you want in. You’ll need either variable speed projectors or ones that have been modified to be variable speed (silent films are usually meant to be projected much slower than sound films, apart from very late ones, which are generally fine at 24 fps). You’ll need a 1.33:1 mask for the projectors, since these aren’t widescreen films you’re working with. And, of course, you’ll need a copy of the film. Films still under copyright can be licensed from distributors, which may also have collections of public domain titles, but a better sources for those would be to ingratiate yourself with local film collectors. You can also acquire titles from the Library of Congress and other film archives. You’ll need someone who can operate the projectors and perform reel changes. I can’t think of any archive or collector who would allow their film to be put on a platter, they’re really hell on film.
In either case, you’ll need accompaniment, either a piano or maybe a quartet. Whoever you hire, make sure they’ve actually accompanied films before. It’s a special skill that, although many a trained and accomplished musician thinks he can manage, takes a great deal more than simply being able to play an instrument well. Check around, most areas have local silent film accompanists that will be more than happy to participate. You’ll probably want someone who can improvise the accompaniment on the spot, it’ll be much easier than having a score composed (if you’re showing a later Chaplin film, bear in mind that part of licensing agreement is that you will use Chaplin’s score for it without alteration, so that does complicate accompaniment matters).
If it’s a foreign film that you can’t find with English translation, you’ll need a reader, who translates the titles aloud as the film runs.
For a film or video source, you might have a look at Kino’s offerings. They offer film on 35mm, 16mm, and video. Kino doesn’t list prices, you’ll have to contact them, but as I recall, it’s 50% of your ticket sales, plus between $100 and $1000, depending on the title. But, if it’s a public domain title you want to show, I’d start with local film collectors first. You might very well find someone who’ll loan you a 16mm print for free.