No, AIFF is fully uncompressed with zero loss, you made the correct choice. You're in a good position, DAC technology changes fast, which means they depreciate faster than speakers, amps, and analog gear. If you have a budget in the neighborhood of $2k, you can get a lot for it.
i cannot speak for all the myriad DACs out there, but I can speak with confidence about my setup, which is excellent.
PS Audio Perfect Wave DAC mk II
($4,000 new, $1350-$1450 used)
Mac mini, external hard disk, $90, basic but high quality Transparent USB cable.
CDs ripped in AIFF, some high res music files in various better than CD resolutions, subscription to Tidal HiFi with full CD quality streaming, music control software by Roon.
this seems to all be within your budget. This setup sounds absolutely outstanding. I'm sure there are several ways to get better sound, but this keeps fairly close pace with my analog rig worth $7k!
I very highly recommend Roon software. Simply amazing. I also recommend dropping Spotify in favor of Tidal Hifi; you can't beat uncompressed!
hope this is useful info, enjoy!