True active speakers + sub out / VS true passive system?

I came into possession of a PA-120 and need a pair of true active speakers with sub out to work as my computer rig for movies and music but I've got a few questions and need some recommendations.

1) Would a true passive system = better audio quality per $ value? I'm thinking a USB DAC/T-Amp (Toppings or Trends) to a pair like BIC DV46si but none of the amps are rated for much wattage or would match up with the sub (am I mistaken here?). Ideally I'd like a headphone amp out as well but its not a deciding factor.

2) $300 is my rough budget cap but I'm willing to spend a bit more if its worth it. What are some true actives that would work with the sub?

3) I was also looking at the Behringer UCA202 or Turtle Beach which I've read sound decent but are they true DACs or will it work for my needs?

I'm open to used equipment as well and so long as the budget is close, maybe like 250/150 for speaker/DAC. I'd like a passive system since its scalable but matching equipment is likely something I won't want to spend much time on esp. with little desk space to spare. My music tastes vary wildly from instrumental, ambient, IDM, "dubstep", alternative, folk etc so I'd prefer something musical that's versatile and does well with vocals.

Also forgot to say I'm doing everything from a laptop (Thinkpad T60p) and may continue doing so (Macbook Pro) unless a desktop falls in my favor later.

Just some speakers I've been tossing around/considering:

Audio Engine a5
M-Audio BX5a
Behringer B1031A
Swan H4
Swan D1010MKII 08
Fostex PM-1

Mauricio: That flow is what I understood it as too but the A5s have a sub out on the back but it may be model specific.

My original consideration was for the Audioengine A5s but since I heard they're not true active speakers I wanted to look for something else.

Huge price gap between the HRT and Behringer though but I'll consider it though I'd still need some way to split the HF/LF signals.

My room is quite small and the sub is overkill but what kind of RMS should I be looking at to fill a roughly 12' X 12' room on the bookshelf speakers? A5s are 100W but so are the H4s.

This is also completely subjective but I keep hearing of the KRKs but think they look pretty gaudy, not something I'd want to look at on my desk every day.

The back of my sub looks like this, no outs and just a crossover, phase and volume knob. I guess its not an active sub but rather a powered one?

Edit: Another thing I was thinking is that I wouldn't want a true HT system with the sub cutting out the low freqs or have them split between the desktop speakers so I could still make use of them without the sub waking the roomates.

Would audio cable splitters degrade the sound quality if I'm running that HRT DAC especially if I get active speakers or if I get a small amp like Dayton DTA-100/Audiosource to a set of passives?

My setup currently with the missing stuff in brackets:

Computer source -> [DAC] - [Split to] -> Sub + [Bookshelfs]

or

Computer source -> [DAC] - [Amplifier] -> Sub + [Passives]

The first option seems simpler and cheaper so I'm leaning towards that more, especially with my budget.

Sorry I was wrong, the sub does have an out. The white is IN and the red is OUT. So essentially it's a mono RCA connection? What use is this for and does this expand my options?

So theoretically, I could forego stereo sound and just pipe music from a DAC to the sub then back to a pair of actives?

Now I'm starting to regret not getting the BIC V1220 a little. BASH amp and full speaker OUT and amp IN.