It is all about preference.
IMO, you should go stick. If you can play stick you can play any fighting game, like Street Fighter and the various 2D Fighters.. but that being said people like Snake Eyez have shown that you an be a top player and still use a pad.
Still in my mind (as I am a old fart) the Stick is a more pure way to play. It is a thrown back to the arcade days and I personally love the feel of the stick, they look awesome and you do not get those terrible cramps, or strain injuries, or calluses you get on pads.
Though if you are looking for "advantage" then mastering the Hitbox can give you huge advantage in NRS games specifically. Insta Air guns that hit in the chest... no problem. Hitbox takes some getting used to but I do not think it can be argued that it has the easiest precision inputting.
Still the real truth is that the "tool" dose not make the "carpenter". No input device will suddenly make you good at the game. Anything you choose, if you get good with it, will be "the best" for you.
I still vote stick though...
I'd recommend the "Drone". It is a good entry level stick, not super cheap but not super expensive like some of the crazy ones that are around. Qanba make some great sticks. If you have been watching evo you probably have seen the add they have running for it (was going to put in thread but couldn't find a youtube of it) so you know it looks frickn awesome (well it dose imo)
So yeah.. go a stick and get a lower-middle cost one to start with like the Drone.