bare cable/banana plug speakers to numark controller

Nope. Those banana plugs require amplifier power. So you are missing the amp in that setup. The amp will usually take RCA outputs and then you run speaker cable to your speakers. I doubt that going out and buying an amp and all the necessary cabling is a good idea.

Do you intend to use the speakers only for practicing? In that case it pays to get a set of decent monitor speakers. Depending on your budget you could look at something like the M-Audio AV40s (better than the Logitech you have now I am guessing) or KRK Rokit 5s or 6s. And there are plenty of reviews over on the blog for more monitors in all kinds of price ranges.

Buying a pair of small, used, PA speakers is also a cheap option to get started.

You are running your controller sound back into the soundcard of your PC? There is a very real possibility that this is what causes the humm. Very unlikely the controller will produce that. Assuming the controller has a built-in soundcard (all but the lowest end do), it’s always better to hook up speakers directly to the controller.

Getting a solid pair of monitor speakers (or as I said a pair of 10″ used PA speakers, which you could also use for the house parties you’ll undoubtedly be asked to play in the near future if not already) is a good plan. Just make sure you get active speakers with the amplifiers built-in. Don’t want to mess around with seperate amplifiers if you don’t have to, imho.