Reddit mentions of Sony HTXT1 2.1-Channel TV Base Speaker with Built-in Subwoofer

http://www.amazon.com/Sony-HT-XT1-Channel-Built-In-Subwoofer/dp/B00IWQREOE

TV goes on top, would look n sound better than stuffing something in that shelf

Sounds like you're going to have to the 2.0/2.1 route. This means an amp/AVR(audio video receiver) and a set of speakers (2.0) and maybe a subwoofer added in (2.1).

Another option would be to get a pedestal system/soundbar or some other all inclusive system. Less fuss, less cost, higher wife acceptance score, lower sound quality. The question is what do you want to do? It sounds like you're all about the quick and dirty so I'll focus on those options first.

• If you want just one single unit then the soundstand/plate/base is the way to go. Examples: LG LAP340, Onkyo LST10, Vizio S2121w, and Sony HT-XT1 all around $200. One optical cable from the TV and you're done. No external subwoofer to sync, link or plug in. Sound should be "uh".
  
  
• Soundbar (Gasp!) "You can really be talking about a soundbar!" Well sub $300 with no wires beyond the TV cabinet...Soundbar. Here is what I say...get one with a wired sub, no more than $200, bass and treble controls. If the wife won't let you get one with an included sub then don't get one. Another option like this would be the Boston Acoustic Cinema set for $180. Again if she won't go for a sub you're out of luck with this as it's the heart of the system.
  
  Now back to the good stuff. AVR + Speakers is the way to do it right. If the wife won't let you get an AVR like this Denon refurb then you're done, see above options. If she will then you're in business to get a better system. Now you have get some speakers to go with your AVR. Here are some that would work good for you Pioneer BS22, Fluance SX6, and Infinity P163 but you have to get two of these and the Polk TSI100. All of those should be below $300 with wire and optical cable.
  
  "But Arm you mentioned a 2.1 didn't you?" why yes I did. AVR $130 + Speakers $50 and a sub. Now add in the wires, and cable from above with this sub cable and you're just at your budget. However, you now have a system that should sound pretty freaking good.
  
  

Excellent, thanks for the info! Just a follow up question - this is the sound base I have: http://www.amazon.com/gp/product/B00IWQREOE?colid=3NIWWRTEY37OD&coliid=I830PTAXQDZHJ&ref_=wl_it_dp_o_pC_nS_ttl

Does a 3.5mm cable go into the ANALOG IN port, or am I stuck having to use HDMI?

These are just 2 examples. I'm not sure if they sound decent or not. Just something I've looked into for my parents quickly. They both feature built in "subwoofers", not sure how effective they would be, but it's something most sound bars don't include internally.

http://www.amazon.com/Sony-HT-XT1-Channel-Built-In-Subwoofer/dp/B00IWQREOE

http://www.amazon.com/LG-Electronics-LAP340-SoundPlate-Bluetooth/dp/B00FQEE0T2