Hello gotog. Sorry for the delayed answer.
I suggest going in small steps. I did that, and being a non-pc-techie I'm happy I did. Plus computer audio opens the door to maybe unimagined options.
You don't need much computing power to play music. But using a dedicated computer allows you to turn off many programs, and features that induce electrical noise inside the computer, so it's the preferred method. If you can get a hold of an old laptop, even with Windows XP, that will do.
I see you have several Apple devices. I have iPods, iPad, iPhone, but no computer, so can't really talk about it. Some people swear about their Minis. Maybe buy a used one to get your feet wet?
For playback you need a software. I use JRiver Media Center and it's good. You can install JRemote on your iPod or iPad, which is an app to remotely control JRiver.
the key feature you want in your DAC is asynchronous USB. You will connect the DAC to the computer through USB. The computer is an electrically noisy environment, though, and the internal clock is all over the place. On the other hand, the internal clock of the DAC is in a very controlled environment meant to play back audio, and asynch USB forces the computer to use the DAC internal clock, reducing jitter. I've been off the DAC merry-go-round for a while now and don't keep up with all the news, but I'd say look into the iFi products to get your feet wet under the stated budget.
where will you store the music? One approach is to stream. Make sure you can get enough definition.
If you wanted to digitize your CDs and play them back: I recommend dBpoweramp for ripping CDs onto a hard drive. And if posible try and avoid using a USB hard drive. The issue is USB stands for universal serial bus, so processes happen in series. If you are playing back audio real time to the DAC and in series you are accessing the data, well that's not optimal. It's not a deal breaker either! Initially I was doing that with my Win XP laptop.
PC playback is all I do now. I sold my CD player because I just wasn't using it anymore. I built a server designed for playing audio only (looks like just another audio component) without screen (I use JRemote in the iPad) no fans or hard drive motors, super optimized the software, and it's the best palyback I've had. I then tried a unique piece of software to run digital room correction and evntually was running digital crossovers and biamping my speakers, liberating my tube amps from having to reproduce the bass. I now find myself at the quandry where I'm realizing I'm getting better sound without my beloved Lamm pre in the chain. I'm heart-broken! I thought it would never leave my house. But my ears suggest otherwise...
I hope this helps