I'm kind of disappointed in what's been offered for the price range OP is looking for..
you want to put out some extra money into three things when you're getting subs, IMO. Subwoofer(s), amp(s), and the box. Besides that as long as your HU (or EQ/line driver) is giving you a clean high RMS voltage signal and you have the crossovers set properly your system should be towards the higher end.
So what to look for when it comes to subs?
Consider the power handling(RMS), impedence, diameter, mounting depth, and freq range - match your amp to these speakers
Quality brands of subs (IMO, you might like others, there's no way I've heard every different sub/amp combo... take this as a point in the right direction)
Entry level -
Alpine - balanced SQ/SPL depending on the model of the woofer
Kicker - mostly SPL subs, no SQ (some models)
JBL
Middle of the road subs
sundown audio
there's a couple more I forgot.. I'll add later if i remember
hertz (arguably high quality, depends on the line of speaker, I like hi energy personally)
loud SPL oriented subs
digital designs
mmats audio
What about an amplifier you say? (Keep in mind, YOU GET WHAT YOU PAY FOR)
Look for 1 or 2 channel amps, mono block class D for high efficiency, with a min imdedence of 1 ohm per channel, or bridged.
My top choice is alpine. I've never run their mono blocks but judging by the quality of the 4 channel alpine I ran for 2-3 years I have no doubt they put out their rated power with less then rated THD. Downside is they can be expensive.
Powerbass is what I've been running recently though, and I think they're great amps. However I believe they did discontinue the asa1000.1dx line that I've run. They put out their rated power. Other amps I would recommend considering are Polk audio (new class D models), DD, and hertz.
So you took all your time figuring out what subs and amp you want, but what about a box? This is one of the most vital components of your system. Depending on your style of music, you'll want a sealed or ported box.
Once you decide what type box you want, consider either building it yourself or having it built custom. (pre fab boxes are mostly junk and will leak)
A custom box can you net you anywhere from 3db to 9db of gain depending on the type of box, and it isn't usually too expensive to have one built. The difference between a pre fab box and custom built box are night and day, invest in a long lasting, awesome sounding box to begin with. Get it built for your subs, with the recommended air volume kept in mind. This obviously varies depending on what sub you pick.
if you want any sort of low bass with authority, I'd recommend getting at least a 10 inch sub, 8 works, but 10-12 are a good middle of the road and will play low with better authority.
This information is all my opinion and comes from the countless hours of research I've put into my own car audio system. I can't guarantee all the information I said is 100% accurate or up to some peoples "par" when it comes to brands or preference. However, I hope I was able to outline information in such a way that points the OP or anyone else reading this in the right direction. If you need more information feel free to ask me and i can share some of the resources I utilize with you.