If you look at wireless options for both inside and outside of the house (with option to different streams inside and out), you are looking at some expensive systems like eg
these (Full disclaimer: I have never tried these, nor I work for them).
I would suggest visiting a brick-and-mortar store, and talking to a salesman about solving half of the wireless problem. There are "home theathers in a box" where some speakers are wireless, and even some systems which are compatible with your record player (you need PHONO input on that system). You will also want a system which supports ARC (Audio Return Channel) so that you can listen to TV programmes coming from your TV.