looking for advice on budget subwoofer

You need to more specific about what you feel needs improving. I assume you want more bass. For $300 you are not likely to get any sort of sub that will enhance 2 channel. You may look to better speaker and/or interconnect and or power cables - they will generally make a big improvement for a modest investment.

Yes...a sub will improve the sound by providing a foundation to the music. If you cross over appropriately, and the sub has a built in amp, you will free your amp to drive only the mids and highs which will greatly improve with the subs addition. The quality of the sub is not that important - any powered sub will do the job.

http://www.audiogon.com/cgi-bin/cls.pl?homesubw&1319484164&/Yamaha-soavo-900sw-birch-new-a

There is a great REL sub listed for $325

Look for a Parts Express KIT sub.

I have a budget system I use in the winter, and I was able to get a Mirage subwoofer on sale for under $300, that is very musical. Vanns has the following subs marked down that are in your range:

Yamaha Soavo: $400 (retail was $1,400) - This would be my choice - 18hz!
Mirage MM8: $350 (retail was $800)
Velodyne SubContractor Series 12: $400 (retail was $800)
REL T3: $400 (retail was $600)

Hope this helps,
mot

One more. HSU Research has a sub on sale that fits in your range.

http://hsuresearch.com/products/stf-1.html

Mot

A used Martin Logan Dynamo is an incredible sub for around $300.
Do not waste money on speaker or interconnect upgrades and run from anyone suggesting upgrading Power cables, a complete fraud.

I would offer a differing opinion than Grege that people who recommend cable upgrades are frauds.

I rely on reason, logic and evidence...not conjecture. Here is a simple, measurable, example that I experienced in my system. My amplifier was running hot to the touch. My friend Bill suggested we use some better speaker cables to lower the resistance. I was using some 12awg cheapie cables. So we bought Military Spec, 12awg, silver-coated copper wire, with teflon coating off ebay. Cost me maybe $60 total. Using a drill and a vice clamp, we twisted them ourselves.

We set up an SPL meter to measure any differences in sound level (at the exact same amp output, and same SPL meter location), before and after the new cables were installed. The simple change in cables resulted in a 3db increase in sound level, and the amp no longer ran hot to the touch. Where I used to run it at 1/2 volume...it was now at 1/4 volume for the same loudness. I won't comment on sonic differences, as that is subjective. But needless to say, there are measurable differences that cables can make in capacitance, inductance, and resistance.

I bought a Zu Audio Bok power cable for my subwoofer off ebay for under $100. Mainly because I know that when there is a dynamic sub signal, the resistance in my power cable won't be a bottleneck to getting ample power to the sub.

Then again...maybe I'm a fraud. :-) Test these things yourself and see.
Mot