I think going 2.1 with your needs will be a bit ineffecient.
I think you’d be better off either going with ab audio amp and 2 big speakers either floor standers or big speakers on stands. You’d have to do the ps3 using its audio stereo output surely thats fine as its stereo only on output. We use to have this set up and it sounded good, paricularly with music. Decent big speakers and you won’t need a sub woofer. We use to have this but binned it as it was blocking the view out the window
Or go with a reciever and 5.1 speaker sytem. We have a Onkyo tx 309 and Bosten acoustics xs speaker package. Its way better with movies and tv than the old hi fi. Its atmospheric and easier to hear what people are saying. You can attach a turn table provided the turn table has a built in pre amp. It would be under budget for you. Although its more wires its tidier as the speaker are wall mounted