Just a kind of beginner question, I suppose. I am a beginner DJ looking to do some live shows, and am debating a good PA system. I would mostly be thinking some school dances and bars, so nothing over powering as we're not working with spaces too big, but I was wondering if two k12's would enough, or if i should add a Ksub, and if so, how would I do that with the Traktor s4,
Which brand you go with is ultimately up to you, I personally am a fan of the QSC K stuff. Used it a bunch, love the sound-features-price equation.
There is no reason not to start out with a pair of the K12. Then as you move to larger gigs or decide you need more power, adding the sub.
From the S4 to the K12, its a straight cable run, buy or build quality cables. (Look into audio and power combi cables) If you are using the Ksub, the K12 has a setting 'extsub' that filters the low end out. leaving the sub to do that work.
Do yourself a favour and get covers (buy/made) for the speakers so they are protected when you are bumping them in and out. Also get a case that all your cables and power strips live in, velcro ties on all your cable as well. Set up this way from the beginning and make life easier. High paying classy clients don't want to see ratty scratched gear and a plastic bag of tangled cable...
In terms of how you hook up, your 1/4th in OUTPUTS are balanced, so buy/make some 1/4th TRS to XLR adapters, and just plug those right into your Ksub's left and right, then do as described above.
Almost all powered portable lower-cost systems are like this, regardless make sure you do NOT connect via RCA or other unbalanced connection. For some unknown reason everything DJs use is unbalanced, which is more prone to signal interference which can (will) degrade your sound quality
I own a lot of K series stuff including 2 pairs of ksubs. I like them for what they are but I dont know many djs who would be happy with them. I would look to get a kw181 instead which isnt much more money but is a lot more of what a dj is looking for, deeper lows and some impact.