Assuming you're not (yet) processing your own film, you'll want to start with a color negative film; there's a good likelihood you can still drop that off at a local pharmacy or Walmart to be sent away for processing at a good price. Be sure to check "return my negatives" because otherwise all you'll get is prints and a CD or thumb drive with fairly low quality scans.
Kodak offers Pro 100, Gold 200, and something in 400 speed (I've forgotten the trade name) in "consumer" films, Ektar 100, Portra 160, and Portra 400 in "professional" films. Ilford has XP2 Super (black and white, but processed in C-41 like color negative films), and Fuji has Superia (at least 400 speed, not sure if they still produce/import the other speeds). There are also a few other choices from Lomography, but they'll be more expensive than the Kodak or Fuji consumer films.