I use a Logitech extreme 3d pro. It's got 10 buttons, 2 triggers, a throttle control, and a hat stick which is set to power management by default.
It's also quite cheap. It's got everything you need, nothing you don't, and it's less than 50 USD. It's not the best. It's quite basic, but it gets the job done. Makes me want to tell stories of nailing an NPC Anaconda with a class 2 plasma accelerator and killing his shield generator in one shot.
Also note that you'll still need to use a keyboard for some functions. I don't imagine many joysticks have enough buttons to actually do everything that needs to be done in Elite.