Glass primary and secondary.. and either carboy caps (to siphon using a pressure differential) or an auto siphon. Get some no rinse sanitizer - star san is a must have. You'll want a hydrometer as well. Get a good sized pot.. preferably 5 gallons (larger if you plan to do all grain in the near future). You'll also need the small stuff like bottles, caps, capper, tubing, drilled bungs and airlocks, carboy brush.
While a turkey fryer is not really necessary since you'll be doing concentrated boils using extract (and maybe steeping some specialty grains) you don't really need the fyer. Now, if you get a turkey fryer you're very well off on your way to all grain brewing which will make the best (and cheapest) beer. The only other thing you'd really need is a cooler and a coopper manifold and you could go all grain... oh, you'd need a chiller too.
Read the "how to brew" link - it really is a great read for beginners and experts a like... www.howtobrew.com