on the cheap

The problem is that your portable device is then tethered to your system 

I get what you are saying..it's not a device for me. My thoughts would be if you do a lot of Bluetooth to your stereo from your phone. I personally don't really use Bluetooth for my music listening or use storage devices. All my music is either streamed from Quboz or from TV app's to Dac. My TT is collecting dust on the sides & I've taken my CD player out of the chain. Albums to me have the sound quality & presentation between and beyond the speakers that is the most enjoyable or realistic...but the convenience of streaming is hard to beat for me. I did just turn 50 and haven't always been a fan of digital in general. I've only been streaming for a little over 2 years now.. slowly learning how to improve the sound. 

I use Bluetooth in car, with portable listening, and I also I have a Sony Bluetooth brick that I use in the kitchen, back patio, and bring occasionally on vacation.  I purchased an Audioengine Bluetooth receiver over 10 years ago for the mid Fi system in our living room that rarely gets used, primarily when one of my adult kids are over and wants to play music from their phone.

  I use AirPlay and Chromecast to stream Apple Music, both of which are better than Bluetooth.  Streaming is secondary to me vs Physical Media, but the OP said his sister would be happy with Bluetooth, as indeed most of the population is, minus those of us that post here

I would consider a pre owned Bryson BDP Pi. 

@goofyfoot for couple hundred bucks (OP’s budget)?!