Transfer CD collection to HDD; play through amplifier; control with iPhone

I'd appreciate help finding Apple-friendly software/hardware that would allow me to burn my CD collection to my Mac, using Apple Lossless quality in iTunes, and then save this collection to a portable hard disk, which I could plug into my good amplifier and speakers for a CD-quality experience. I like Apple Music but want to go beyond the compressed codec. Ideally, I could catalogue the collection with a nice interface similar to iTunes/Apple Music. I think it's likely that sound would be best and most reliable if the connection between the HD and the amp was wired (USB3?) but I'd like to be able to use the iPhone as a remote to select the song, connecting with the HDD wirelessly. Is there an Apple setup that would allow this sort of thing?

Thanks, James

(I'm generally using all the latest Apple software, but my Macbook Air won't be able to hold my CD collection; hence the need for a big-capacity external drive. I have a WiFi router supplied by my ISP, even though I like the look and sound of the Apple AirPorts - perhaps they would be the thing, given the combination of networking and storage?).