OP…”Here is another way to consider my question. Are low cost DACs (such as the Schiit) going to be any better than the DAC in the Apple Airport Express?…”
The 2 DAC’s mentioned by @pmm are an excellent idea. I purchased an early edition Schiit Uber Analog DAC as my first. I used a stripped down laptop with an external power supply and a Cardas Clear usb cable. I upgraded to a Schiit Yiggy, and later added a Project Stream Box Ultra II and ditched the laptop. I also have a Cambridge DAC Magic 200. I gifted my son the latest generation Blue Sound Node to replace the Bifrost I had given him when I upgraded. He runs a simple system of a vintage Marantz receiver and Klipsh KG speakers. Switching from blue tooth to an entry level streamer like the Blue Sound was an huge improvement for him. Also consider switching to a source that’s not blue tooth. If you don’t want to get an additional streamer, get the Node or something from IfI. Having your system hardwired to the router and the cable that feeds the DAC have a significant influence too. Happy hunting, Mike B.
I have a Bluesound NODE streamer and a Denafrips Are II DAC.
Given your budget, I would suggest that a used NODE (which has a built-in DAC) would give you the most bang for the buck. Especially if your hearing or system isn't top-notch, you'll find the NODE's DAC quite satisfactory, and you can continue to stream via wi-fi--the NODE is really designed to work well that way, and it does when you give it a strong wi-fi signal. The smartphone app for the NODE can also tell you the wi-fi signal strength it is receiving, so you can know whether it is strong enough to stream high-resolution files or just CD-quality files. And I can hear that hi-res files sound better than CD on the NODE, even using its DAC.