Watch the Tones and Gear online guitar lesson by Jason Loughlin from Focus On: Travis Picking
As far as tone goes, I try to use a good clean tone. You want the clarity and nuance of the picking to come out. Some player prefer to play this stlye strickly on acoustic for that very reason. If you're a more of a Chet Atkins or Rockabilly fan you may prefer an electric. It really doesn't matter a great deal as long as you're getting a good clear tone out of the instrument. The only effects that are associated with travis picking are slapback echo and reverb. Any delay pedal is capable of giving you a good slapback. You want to dial in one short repeat. This style is known for using a thumb pick. While it will help you get a very clear and strong attach with your bass notes it's not mandatory that you play with a thumb pick. What kind of thumb pick you use is up to you. Try a bunch before settling. Also, try a bunch of the same sizes. Not all mediums fit the same. Make sure it fits snug without cutting off circulation.