Yes to all questions (assuming you don't have a CRT). I went tag sale hopping last weekend and after about an hour found two CRT's for ten dollars.
As for the copy if you have a wii then download the 20xx hack pack, although I think that may be technically illegal if you don't have a copy of the game. If you don't then it still might be cheaper to get a wii than to buy a copy of Melee. You can mod the WiiU too but that may lag, maybe someone can clear that up or you can ask it in the technical issues thread if you're interested.
The controller is very, very important. You need all the buttons you use to function well (I don't use R or X so if they didn't work I wouldn't care), and you need a firm stick. Buying a good one can be a pain. Do not go to Gamestop or buy any third party controller for that matter. If you are just getting into Melee you can get a $40 smash 4 controller, but I personally have experienced fast stick deterioration and I know others have had issues too. I'm not really sure where to find a good controller so I'll link a recent thread about finding a new controller:
http://smashboards.com/threads/are-the-newer-controllers-problematic-for-melee.400292/
If you just want to play the game casually nothing really matters other than maybe the controller and getting a copy of the game of course.
