If you like 4-decks, then you’d best get a 4-channel controller. Not really worth the trouble otherwise.
Choice of controller though starts with determining your workflow, picking the best software for that workflow, then setting a budget and finally picking 2 or 3 controllers that fit workflow, software and budget.
Picking things before you really know what you need/want or because “you have heard about a brand)” is really a bad idea. What I might find the perfect solution might not work for you at all and the other way around. So it’s impossible to advice you on what will work specifically for you.
Same goes for DJ software, they all have their pros and cons and one mans con can be other mans pro. There is simply no such thing as THE BEST software, only software that is best for YOU.
Pulselocker (the streaming software) is not free as far as I know but has a subscription plan.
Some things to wonder about:
1) As a beginner do you want to focus on 4-deck use or do you want to get all the basics down correctly first.
2) If you really feel you need 4 decks on a regular basis, would it not be better to have 4 actual decks (for example adding two mediaplayers or single deck controllers to a 4-channel standalone controller?
3) Why do you want streaming service? Is it for music discovery, is it because you don’t want to buy/own your tracks or is it because you feel you need access to the whole world collection of music and then some?
If you don’t have a controller yet and you are not all that sure what you need/want in a controller yet, I’d stick with a 2-deck/2-channel starter controller and get all my skills and collection in order. Then, by the time you are ready to upgrade, many of the questions you ask now you will have figured out the answer to yourself.
Our usual suspects for starter controllers are (in no particular order):
General DJ Software support:
* Pioneer DDJ-SB2
* Numark Mixtrack Pro 3
* Reloop Beatmix 2
* Denon MC2000 (or MC4000 depending on available budget)
Traktor software
* Traktor S2
RekordBox DJ
* Pioneer DDJ-RB