On a $400 to $500 budget, I'd skip the subwoofer and get a pair of Behringer 2031P's (with 8-3/4" woofers) for about $180 and Factory Reconditioned Onkyo TX-8555. That leaves enough money for a basic CD player.
http://www.bhphotovideo.com/c/product/321817-REG/Behringer_B2031P_B2031P_2_Way_Passive.html
http://www.accessories4less.com/make-a-store/item/ONKTX8555/Onkyo/TX-8555-100-watts-2-channel-Stereo-Receiver/1.html
I think this set up will give you better overall sound quality than finding cheaper speakers or reciever and getting a sub.
I need to follow up on this and point out that the Behringer 2031P is a 4 Ohm speaker. The Onkyo above is rated for 4 ohms. I would be reluctant to pair these speakers with the Sherwood receiver. Maybe the Sherwood would work, but I haven't seen any mention of it and 4 ohms in the specifications, so it is best to assume not.
A few months ago, I bought both Infinity P362 and Behringer 2031P out of curiosity. Both impress me as amazing sound quality for less than $500 speakers, but, to my ear, the 2031P is the better speaker. The point is moot because P362's would blow your budget.
However, from reading the other postings, I'd like to elaborate on my recommendation.
Although I have never personally heard the Behringer 2030P (it is in the same series as the 2031P), because of all of the 2030P recommendations I see here, I have to believe it's sound quality is on par with the 2031P. The 2031P offers more bass from the larger woofer; however, in theory, the smaller woofer of the 2030P should offer more detail than the 2031P in the upper midrange. Having heard how much detail the 2031P offers over the highly recommended 3-way Infinity P362, I can't imagine the 2031P loses
too much detail to the 2030P.
However, the 2030P's are 8 ohm speakers and can be comfortably driven by a receiver such as the Sherwood. Since you save about $130 by getting the 2030P's and the Sherwood Receiver, that is enough to buy the Dayton subwoofer. This would give you a 2.1 system with excellent sounding speakers, in budget. But, in my experience, in terms of absolute sound quality, subwoofers can do more harm than good.
My first sub was a SVS SB12-plus, which is a very good, musical sub. However, while it added impressive low frequency sound, I was completely disappointed with it because it blurred the detail and articulation of my speakers! I could tell this happened in the lowest frequencies. Replacing the SB12-Plus with a pair of Martin Logan Dynamos yielded a substantial improvement. Two subs better balances the room modes and the Dynamos roll off before they reach the lower frequencies. I guess both of these factors played a part. Later, when I moved the SB12-Plus to a different room and managed some EQ, I am finding it is a very good sub- but it was a one note sub in that first room without advanced EQ.
Don't get me wrong! A properly executed sub is a
wonderful thing, but a
properly executed sub requires a pretty good investment of time and money.
Here is a video on room modes:
http://www.audioholics.com/news/trade-show-coverage/video/thx-managing-bass-modes
And here is a calculator you can use to assess your room:
http://www.hometheatershack.com/forums/home-theater-design-construction/337-room-mode-calculator-converter.html
Ultimately, my original recommendation is still the solution
I would choose as best SQ under $400, but that is one experience/opinion and there is a lot of knowledge on this board!
PS - You don't give a location, but if you are in close by, I'd be happy to lend you the Behringer 2031P's to try out and see what you think about using them without a sub.
Cheers!