JLF sticks are the best, there’s no denying that fact, but when it comes to hooking one up to a 360, there is another stick available you could use depending what pad you are using.
If you are using a common ground Madcatz wired controller or official M$ wireless controller, the JLF is the easiest to hookup.
If you are using an official M$ wired controller, they don’t have a common ground setup in which case you will have to hook up two wires to each direction on the stick. In that case a JLW stick might be a better option for you as it doesn’t have a board attached to the stick, you hook up your wires directly to the micro switches. You could also use this stick with a common ground controller, you just have to daisy chain the grounds, that’s all.
The JLW does feel different to the JLF’s though, it’s more stiffer and tighter IMO, which may or may not be a good thing for you, but it is another option.
As for mounting plates, the default one is the flat metal plate. You could use any of the others, depending on your case design.