Hi Andrew, I used a Telecaster guitar and a Fender Princeton Amp for Reelin' in the years. If you don't have a Tele, any single coil pick will get you very close! If you don't have a single coil pick up try your bridge pick and pick closer to the bridge for a brighter sound!
As far as amps, anything with a bright and tubey sound will do. Fender or Vox, even a Marshall dialed in right will do. Use your ears, fingers and best judgment! Most of all, have fun!!!
Cheers, Tom~