[cel4145]

You can always split the audio coming out of your computer and run it separately to both the powered speakers and your Polk sub. The problem is that you'll then need to set the low pass filter on the sub to the low roll off of the speakers, whereas you might get better bass from your setup using a higher crossover on the speakers. Audio/video receivers have bass management that takes care of all that (unless you buy an AVR that is really, really old). Some powered monitors have 80hz high pass filters that can work as well where you then just set your sub high pass filter to 80hz; many don't in your budget range.

Neutral speakers can be made warm sounding if you use an 80hz crossover and bump the bass, and since you like hip hop and electronic music, that will probably make you very happy

Studio monitors are generally designed for music listening nearfield and will not sound harsh. The Ascends are neutral and not harsh.

 

[cswann1]

If I were in your situation, I would try to avoid buying an older, used receiver.  You always take a chance when buying used electronics, but even if it works fine, they are still very bulky and sort of overkill in a 2ch setup.  
 
Since you have a sub, I like the idea of powered speakers.  I have no experience with these so I'm not making a recommendation but you might consider the Emotiva powered speakers. This model comes in at your price point.
 
http://shop.emotiva.com/collections/speakers/products/airmotiv4 

 

[marinqf]

Also, if they are near-field speakers, I'm hoping that each of the ones you and I mentioned are powerful enough to work as bookshelf speakers in a small room...

 

[dc5itr329]

  If I were in your situation, I would try to avoid buying an older, used receiver.  You always take a chance when buying used electronics, but even if it works fine, they are still very bulky and sort of overkill in a 2ch setup.  
 
Since you have a sub, I like the idea of powered speakers.  I have no experience with these so I'm not making a recommendation but you might consider the Emotiva powered speakers. This model comes in at your price point.
 
http://shop.emotiva.com/collections/speakers/products/airmotiv4 

 
Agreed.  Powered speakers would be very implement in this situation.

 

[marinqf]

"You can always split the audio coming out of your computer and run it separately to both the powered speakers and your Polk sub."
----How would I split the audio? Would a cheap DAC like the Behringer UCA202 work? Regardless, would you recommend I buy a cheap DAC like the Behringer UCA202?
 
"The problem is that you'll then need to set the low pass filter on the sub to the low roll off of the speakers, whereas you might get better bass from your setup using a higher crossover on the speakers."
----How do I look up the look up the low roll off of the speakers/set the crossover? Do I need a receiver? (I decided I'm going to get JBL LSR305s)
 
Some powered monitors have 80hz high pass filters that can work as well where you then just set your sub high pass filter to 80hz; many don't in your budget range."
 
 
----I ended up deciding to get the JBL LSR305s. How can I look up if these are sufficient to do that?
 
Finally, in order to hook them up to my sub, do I need a receiver or can I just hook them up to the sub and the sub acts as a receiver?
 
Sorry for all the questions, I'm extremely new to this. Here are some pictures that might help:

This image is almost identical to the back of the PolkAudio woofer, except the low pass only goes down to 80 and the peak says 200 (I have no idea what that means unless thats the crossover point). Also above the red and white line in holes there is also a yellow one above it. Finally, the two pronged plug in on the right actually looks more like the 3 pronged plug on the jbl speakers (except there is only 2 prongs instead of 3). The other image is of the LSR305's rear panel. 

 

[cel4145]

"You can always split the audio coming out of your computer and run it separately to both the powered speakers and your Polk sub."
----How would I split the audio? Would a cheap DAC like the Behringer UCA202 work? Regardless, would you recommend I buy a cheap DAC like the Behringer UCA202?

Two of these would take a left/right RCA output and split each channel into two plugs: http://www.amazon.com/Mediabridge-ULTRA-Series-Y-Adapter-Inches/dp/B005DL2OVE/ . Then one from each goes to your sub RCA inputs, the others to your speakers. There are also cheaper versions you could look for. You would still need splitters like that whether or not you buy a DAC.

However, you need some kind of RCA to balanced plug converters for the LSR305s. Not sure what people recommend.

"The problem is that you'll then need to set the low pass filter on the sub to the low roll off of the speakers, whereas you might get better bass from your setup using a higher crossover on the speakers."
----How do I look up the look up the low roll off of the speakers/set the crossover? Do I need a receiver? (I decided I'm going to get JBL LSR305s)

A receiver wouldn't do you any good here for integrating your sub with powered speakers unless you bought a very expensive one (I'm talking $600 or $700 or more). The JBL LSR305s do not have a high pass filter. JBL should have the low frequency range of those speakers listed either on the box they came in or on their product page on the website. However, since your sub's low pass only goes down to 60hz, I would try that. Of course, you can adjust that low pass filter to whatever sounds best to you