Recommendations for a modestly-priced audio system?

My friend asked me to put together an audio system for her to replace her very old system.    She wants an integrated amp that will take an input from her TT.  God knows the condition of her cartridge and stylus!  There are boatloads of integrated amps with BT-streaming capabilities, which, when she comes to her senses, with get a Spotify/Tidal subscription and forget about her 40-year old collection of ragged vinyl.  Maybe not.  The amp needs to be BT-compatible... no extra components.  

Hopefully, the system will be simple:  an integrated amp and a pair of passive speakers.  The budget is about $1K but I could twist her arm a bit to get to $1.5K.  Recommendations for either the integrated amp and speakers would be very much appreciated, relying on the wealth of knowledge that you fellas have.  I will say that she has a pretty large LV room, sort of an "open room" arrangement, and will need speakers to sufficiently pressurize her large room.

Thanks for any and all input.      
Arcam SA10 integrated amp for $799, KEF Q150 on sale for $300, buy a used cheap subwoofer $150. If you are in the Chicagoland area My local store that I buy from has all of this:
if you are not in this area look up a KEF dealer since this is the one thing on sale. I hope this helped. 

My rec of the axr85 is partially based in the ease of connecting iPhone, iPad or Mac via Bluetooth. Just a button on the remote. Also allows adjusting treble bass and balance from the listening position with the remote. The ifizen blue might give a marginally better conection (I've occasionally experienced interference when using bluetooth with my axr100) but the all in one box solution seems simpler and given your friends requirements I'd stick with the axr85. 
I have several Sprout100 and I am very pleased.  The Sprout100 is class D and runs very cool.   However, it does run warmer with my 87db Canton Karat 920 speakers than my 93db Kirksaeter speakers.   Elac speakers are not very sensitive so I would recommend the Klipsch speakers over Elac.   The bluetooth in the PS Audio does not support AptX but that is fine with me as my iPad does not support AptX anyway.   Also the support at PS Audio responsive and timely.
Peachtree Nova 150 used is around $700-$800. I sold mine but it was connected to a KEF LS50 that can be found for about $700. The KEF's fill up my 12 x 20 x 25+ room surprisingly well. Though the LS50s now have Benchmark AHB2 mono on them and they are more powerful than the NOVA 150.

I think the NOVA has BT or some sort of iPhone integration. Peachtree may also have a BT add-on module.
Since the mini Lores are pretty high sensitivity, you don't need much power to get them, here is another option that is well reviewed, has a remote, blue tooth connectivity, phono connectivity, and price of speakers and integrated amp....$1100.

NAD D 3020 V2 Stereo integrated amplifier with built-in DAC and Bluetooth® at Crutchfield