Traditional archery doesn't really require a lot of stuff. You need some kind of shooting glove or tab. I recently started using the Dura Glove ($24.95 from Three Rivers), which I like, or there are many others to choose from. You need some kind of quiver, which is really a personal preference. You can use Cat Whiskers for a string silencer (about $2.00 anywhere), or any number of other string silencers.
Then there is the matter of arrows, which are very important. To get started, you might want to try 2016 aluminum arrows. I would leave them cut long, maybe 30", and use 125 grain points. At the same time you're buying the arrows, get yourself a bare shaft cut to the same length, and make a promise to yourself to learn how to bare shaft tune after your shooting style settles down some. After you learn bare shaft tuning, you'll probably want to cut your arrows down some. Most trad archers use three 5" feathers. Plastic vanes do not work as well if you're shooting off the shelf.
You should buy a bow square and nock tool. You should initially set your nock so that it is 1/2" above square, measured to the bottom of your string nock. You should nock your arrow under the string nock. You will probably want to adjust this after you learn bare shaft tuning, but it is okay as a start.
Shooting split or 3 under is a personal preference. I shot split for 20 years and recently switched to 3 under. If you decide you like 3 under better, raise your nock up to 3/4".