As for lock rings, I prefer Hornady's as they're a split ring design, fast and easy to use. The reason people like them over others is the fact that they don't tighten into the threads of the dies and Hornady's provide more clamping force.
As was said, all dies will get the job done, some are just made better/tighter tolerances. The only time I've bought Lee was because I couldn't get or find other companies dies available at when I needed them. After finding the others I sold the Lee dies off, like I said, they get the job done but have always felt cheap.
Nowadays I look for Redding dies first, if I can't find them then I look for RCBS or Hornady. CH4D makes some nice dies and tools that other companies don't, for large caliber dies they're hard to beat. Their 50BMG dies are the best on the market, they got the rights to manufacture the Rock Crusher press that will load up to 20mm. If you're looking for a specialty die check them out, if they don't have it, chances are they can make you one.
If you buy a Dillon press of any type, buy their dies and equipment. They're designed to work together extremely well, the same can't be said when you mix other companies equipment with theirs. Being that you're just starting out a good single stage press is the easiest way to go. If you step up to a progressive in the future, keep the single stage for load development, just an easier way to do it. Then you can transfer the load to the progressive and knock out a bigger lot of ammo. Sorry for getting a little off topic at the end.