Not really such a thing as a
best joystick for Elite. There are several options. Expensive HOTAS like the Thrustmaster Warthog work really well, but you are looking at over $400 (US) for the stick and throttle. All the CH products work well and are well-made. Many people swear by the Saitek x52 HOTAS, which is around $140. I personally use a gamepad and a Thrustmaster T16000m, pictured below, and have seen several other people on here and Star Citizen that use that combo (like Bix in the last post is similar). That combo will run you $120-$150 depending on what sales you find. The best all depends on what you like and how much you want to invest.
If you are wanting to know what the best stick for the least money is, I think that is undoubtedly the Thrustmaster T16000m. It runs $40-$50, although people have been buying a lot of them with the new boom in space sims, so it can be hard to find them in-stock. Currently Office Depot has them in-stock online for $48 and Fry's says they will ship within the month at $40. It has twist, can be switched to left or right hand use, good stiff spring, uses the same magnetic sensors as the Warthog and can also use the joystick software the expensive Thrustmasters use. The construction and buttons aren't as nice or snappy as the expensive joysticks, but everything still works just fine and doesn't feel like junk. It is super-accurate and I don't regret buying one at all. Love it. The one annoying thing about them can be the green light that lights up any time you move the stick, but it is a 2 minute fix to disable it
(detailed here, with pics).