Need help playing through 3 pairs of speakers - Amp & selector?


I want to play my records through 3 pairs of speakers at the same, I have one pair by the TV & decks (Dayton Audio T65 - 6 ohms), also 2 pairs of polk atriums outside (8 ohms)

Would be great if I could get the TV playing sound through the T65s when needed but not vital

My budget is $300, do I need an amp & a speaker selector box?
If so I would love some recommendations and ideas for amp specs I’d need

Would it be more cost effective to get some kind of 2 in 1 unit if they exist?

Total hifi newbie here

With two pairs, you could get away with hooking both up to one amp and running output A and B together.
For three sets of speakers, I’d say multi-channel amplifier (from the home-cinema area?, or something like this)

Maybe something like 6-channel amplifier would do the trick ?

What outputs does the Rane mixer and Pioneer TV have or what outputs can be used?

Then those available outputs → need to be connected to a suitable 6 channel amplifier that support those with connections. When the needed connections are known comes the budget. Is there something available or is there not. Prices change when properties change.

This is the rear of the Rane mixer:

So rcas or balanced 1/4"

TV audio output would be RCA

Thanks for the reply!