Your existing system (thankfully) has information readily available - and they are 6ohm speakers which were driven by a receiver rated at 50 watts per channel (likely in stereo) at .9% THD - which is very high.
By comparison, the Denon AVR-1912 which is their least expensive 7.1 surround receiver, is rated at 90 watts per channel, at 8 ohms (not 6), at .08% THD.
DENON US)
So, far more power, with far less noise, with a higher ohm rating. Something like this will work nicely with the speakers you already own, and you can expand or change out from there. Or find a similar receiver that may be a year or two old and go that route instead.
There's a bunch of questions which could be asked, but it kind of comes down to your budget and what YOU consider mid level. IMO, what I have is mid-level for my speakers, good for my receiver, and good for my subwoofer. As I said before, a good rule is to spend just as much on speakers as you do on your TV, then ask and do research based upon that budget.
A decent mid-level subwoofer would be an Epik Legend...
Welcome to Epik Subwoofers
Their Empire is a good one. There is still better stuff out there.
Good speakers are all over the place.
I haven't researched sound bars in a while, but Sound & Vision did a pretty good shoot out a year or so ago and pretty much stated that all soundbars were a pretty solid improvement over the speaker built into the TV.
Your old RCA system is not good. But, it's not horrible either. Reminds me of my first Kenwood home theater in a box kit. If it still works, it likely will give you a decent upgrade on the TVs audio as it is. Use the digital audio outputs from your Blu-ray Disc player and your cable box for best audio quality.
Then just start down the upgrade path. New receiver and a couple of new speakers. Add a decent center speaker, and a good subwoofer. Add some decent surround speakers, then you will be all set.
But, the first part is getting that TV, and I would head over to the TV section on these forums to ensure you are making an informed decision on your first purchase and worry about the rest later on.