If you have the budget you said, I would get a Mixtrack pro and save the rest for later.
The mixtrack pro will get you started nicely.
If you really want to invest more from the start, check out the Terminal Mix series. The do not innovate a lot, but they are the best bang for the buck in my opinion. Do not forget to factor in some decent headphones if you did not already get them and check out our free DJ guides and videos.
Now to your questions:
1) Yes.
2) You will most likely want a soundcard. For real mixing you need at least 2 audio outputs (at least) one for speakers and one for your headphones and sometimes an additional one for the DJ booth. Most controllers with soundcards have at least 2 channel audio to do that. (Terminal Mix has Booth out too.) You might want to look for Phil’s video on why you need headphones… Also most soundcards in controllers have much better audio quality than the laptop soundcards.
3) Yes the mixtrack pro is good enough to play infront of most crowds, so is the N4 (however it is all plastic and you could get a metal Terminal Mix at the same price)
4) Djay does support a lot of controllers, but is only 2 channels. It has come a long way and is nice to dj with. However most of the controllers you listed also support Serato DJ Intro, which in some aspects excels Djay and in some not. You can always try both… if Djay does not support your controller natively it has a great MIDI learn function, that will make it easy for you to make your controller work with it. (You need Djay and an Apple Laptop of course to work like that, the listed controllers DO NOT work with an iPad.)
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