Could someone help figure out a setup?

As far as I know Parts Express offers different Dayton subs(8", 10", 12" and the aforementioned 15"). If you purchase the Audioengine  speakers then you might do well with the Audioengine sub.   

At your budget my suggestion would be to purchase the powered speakers 1st and a DAC that will mate to your SPDIF output, optical or coax. Consider the sub at a later date.    

I hope bumping is okay on this forum. I've been unable to get help with this on other sites, or even from the companies themselves so I'm kind of stuck.

My main question before buying is

"Mesch mentions a sub from Dayton Audio being another option then the sub from Audio Engine.
Dayton Audio sub is 15" but only 150 watts while the sub from AudioEngine is only 8", but 250 watts. For deep, clear bass (hopefully in most of the main ranges in metal and rap), is the 15" a better choice?"

Links to both in case anyone needs it

Dayton Audio SUB-1500:
https://audioengineusa.com/product_tech_specs/s8-powered-subwoofer/

AudioEngine S8 sub: https://www.parts-express.com/Dayton-Audio-SUB-1500-15-150-Watt-Powered-Subwoofer-300-634

Thank you everyone for the replies.

As many there seems to be more votes for AudioEngine, and everything looks good there, I believe I will be going for them.

I see people mention a DAC, which I’d be willing to buy if it’s the smart thing to do. Would I just connect my SPDIF output on my motherboard to this DAC? The one mentioned by Fuzztone does have an optical input.

Mesch mentions a sub from Dayton Audio being another option then the sub from AE.
DA sub is 15" but only 150 watts while the sub from AE is only 8", but 250 watts. For deep, clear bass (hopefully in most of the main ranges in metal and rap), is the 15" a better choice?

Lastly: I see AudioEngine also has a "Desktop Amplifier". However, I cannot use this with speakers that are already powered, correct?

Also, I do already have speaker stands and foam speaker padding ready so those would sit beside the desk with the sub on the carpeted and padded floor.

Logitech   Z625 --- THX 2.1 system.

amazon $144.00

Cheers

$6500.00 for speakers and a subwoofer is very inexpensive. Like I said what you are looking for Best Buy has and you can go listen and pick out what you like. For background music I use Sonos gear. A pair of Fives and one Sonos sub cost $1700.00 They make powered speakers for $400/pair but the sub is $700. Best Buy carries Sonos and several other brands. 

Must agree that an inexpensive outboard DAC would be a great improvement over use of the computer 3.5mm output. 

+3 Audioengine. 

Guarantee that this blows out PC headphone jack.
https://apos.audio/products/smsl-m3-dac-amp?_pos=2&_sid=5a925d38a&_ss=rAnd an all important volume control.

All in $682

Sorry Cholly the headphone jack sounds like doodoo.

For speakers the Genelecs are fine but you might be happier with Adams.
Both are bi amped but the Adams go to 39Hz  with a ribbonn on top.
https://www.sweetwater.com/store/detail/T8V--adam-audio-t8v-8-inch-powered-studio-monitor?mrkgadid=3...

If you don’t have a DAC you can’t get there from here.
$650 plus DAC is the most you want to drop on computer audio.

+2 audio engine

The Genelec are always excellent desktop speakers or you could look at JBL. There are desktop stands and pads available as well.

https://www.sweetwater.com/store/detail/LSR308mk2pr--jbl-308p-mkii-8-inch-powered-studio-monitors-pa...

For budget speakers - M-Audio and PreSonus are good brands. Edifier also makes some fairly decent speakers at reasonable prices. As you like bass, some of these have a bass/treble knob on the back. Look for one with AUX (3.5mm) in/out or RCA (if you’re hooking them up to an internal/external soundcard.

Since your budget is limited, powered speakers might be a better option for you. Passive speakers would require an amplifier to drive them.

If the speakers sit on a desk, I would advise getting some isolation pads for them to rest on.

In response to ' information ' the post ( set-up ) revolves around
' Speakers ' .
Active and Passive are two general categories for Speakers.
If you do not have an amplifier to drive ( power ) a set of loudspeakers then Active is the category to look into for ideas.
Genelec is a highly regarded manufacturer for Sound Production Gear.
Model 8320A is a two way monitor in the price range specified @ $625.
8331A would represent a considerable step-up in terms of performance and not necessarily a price point.
Placing a Speaker on a stand rather than on a desk surface would be an important distinction for a higher level of performance.
www.Genelec.com
Audio Engine products also would be worth looking into for selection.

+1 twoleftears.  One could purchase the speakers 1st then the sub later. The audioengine one would be a match, however one could also look into the Dayton Audio subs offered by Parts Express. 

$750 combo
https://audioengineusa.com/shop/poweredspeakers/a5-plus-classic-speakers/
https://audioengineusa.com/speakers/subwoofers/

$6,500 for two speakers and a subwoofer? 

I think you should check out the combination systems at Best Buy or you need to add another zero to that figure.