People still continue to buy the Bose TV Speaker even after we made a dedicated video on it…. To get you to stop, we took to facebook marketplace and gave ourselves the SAME budget and managed to buy a 5.1 surround sound setup with dedicated receivers!
Considering this is the home video section, I thought this would apply to this community. Reminds me of when I had my tiny dirt cheap 5.1 system, which sounded great to me. Especially when playing Bad Company 2 on my Xbox360.
I would always recommend paying attention to your room acoustics. Better speakers than what your TV has will make a difference, but beyond that you need to treat the room.
If you kill immediate high frequency reflections from walls, floor and ceiling to your listening position, and reduce energy of low frequency standing waves, you make a bigger difference than spending piles of cash on new equipment. And if you have a subwoofer, play around with the placement as even fairly small shifts can have a notable impact in your listening position.