You already have the basics.
Now, you know your MP3s are lossy. Lossy is a relative term. Digital, by nature, is 'lossy'. CDs are more lossy than SACD or DVD-A. Some sound better than others, and different recordings have different audio properties. Some will swear by vinyl (records) while others swear by CDs, and others by the better formats like SACD, DVD-A, or audio Blu-ray Discs. Understand that your lossy audio is not going to sound as good as a one-for-one copy of a CD no matter what.
Now, that said, for best quality from an iOS device, you should copy your CDs using ALAC (Apple Lossless) and then to an AirPlay device you should get full CD quality audio from the system quite nicely.
The follow up to all of this is WHY do you think you need 5.1? Stereo audio generally should be listened to as stereo audio. Not surround. Surround sound is for movies and such which are recorded from day one as surround sound mixes. Music is, generally speaking, meant to be listened to in stereo. I'm a big fan of surround sound, but my music comes out in stereo, and stays in stereo.
With that said, your money will also deliver better sound if you stick to stereo.
If you don't intend to ever connect this to a TV, then it changes things some as many A/V receivers these days basically require a TV to set them up properly using fancy on-screen displays. A lack of a TV will impact your purchasing decision.
It all comes down to a good pre-amp, which I would pair with a decent amplifier, and then some nice speakers. I don't track it that closely, but something like an Emotiva UMC-200 and pair it to a decent amplifier. No specific recommendation from me.
Leaving $1,500 or so for the speakers and going stereo would certainly be my recommendation considering your source of music.