Have you thought about a raspberry pi?

You can set one up as a media centre complete with audio/video streaming.

Studio monitors suck for living-room listening. They don't have adequate dispersion, so they only sound right in the sweet spot.
 
I knew a couple who worked at Mackie and won a pair of HR824s in a drawing at the company Christmas party. Not being studio types, they hooked them up to their TV. You'd think a thousand dollars' worth of amplification would sound great, but they'd have done better with a $100 bookshelf system from the pawnshop.
 
That's actually the route I'd take in your situation. Get some second-hand quality passive hi-fi speakers and buy a new power amp if necessary.
 
My TV's connected to a pair of Altec hi-fi speakers I bought in the early 80's. Those are augmented by two modified PA speakers in which I've disconnected the horns and tweeters and installed a good crossover for the 18" JBL woofers only. Is it a flat reference? Hardly. But it does give me an idea what my music will sound like on a hi-fi.
 
And it kicks ass on concert videos and action movies. Good I don't have downstairs neighbors.

Thanks for the pointer on not putting the powered monitors in the big upstairs room.
 
So, it sounds like I need to get an amp for upstairs.  This could get costly, especially since I live in New Zealand, and it's hard to ship a cheap[ish] amp here from the US.
 
 

Here's what I ended up doing:
 
Downstairs (tv room):  I bought a cheap secondhand surround-sound system, replacing its small left and right front speakers with a bigger pair of speakers that I already had.  It sounds fine, and has the bonus of letting us watch TV in surround sound for the first time ever!  The Playstation works find with it, and thanks to CEC the TV, Playstation, and surround-sound system all operate together nicely (for example, the TV remote controls the surround-sound's volume and power).
 
Upstairs (lounge):  I moved my 1990s stereo upstairs, along with my best pair of speakers.  I then bought a Chromecast, which lets us play Spotify on it.  Awesome! 
 
So, the total cost was about $200 NZD (for the surround-system and the Chromecast), which is much cheaper than what I thought we'd need to spend! 
 
Plus, I can sell the second PS3 since we're not needing it for Spotify (since Chromecast handles it).