I started out with the Lee Loader kit, but it didn't take long before I upgraded to a regular single stage press. The Lee Loader kits work, but they are very slow and I found them to be a little frustrating to use. If you want to enjoy reloading as a hobby, I would recommend starting with a press.... you'll end up with one if you continue to reload anyway.
You've got all the components down (case, powder, bullet, primer). In all honesty there really isn't a lot of difference between primers. CCI, Winchester, Remington... they all will work. 308 will take large rifle or large rifle magnum primers, depending on the load you use. Your bullet choice would depend on what you plan on using the rifle for, hunting, target, or both.
A good idea is to pick up a reloading manual... you'll want to have a couple anyway. They all provide good information and show the reloading process step by step. A manual will show you what to expect.