That price range is too low for anything decent. Yes, you can go for the Modi + Magni stack but that is very entry level in terms of sound quality. The Teac AI-301DA has a decent DAC and uses an ICEPower Class D module so sound quality is pretty good, and it only costs $350 from Amazon. The Joutenhiem would be a step up from that, but that's $500 with the DAC module. The sound quality from a DAC is mostly determined by the quality of power supply, input components and the design of the output circuit -- those little USB units everyone promotes on here are awful because they have very low end power supplies, everything is integrated ICs and chip amps meaning the lowest quality possible, even though the D/A chip itself may be no different from much more expensive / larger DACs.
Here, let me drop some knowledge that other respondents are short on:
1. The DAC is more important than the amp, once the amp is at a certain level of quality. Sub-$100 USB all-in-ones are well short of that minimum level.
2. USB is an awful audio interface but you're probably stuck with it; a USB isolator like the Schiit Wyrd or Audioquest Jitterbug is mandatory.
3. Unless you are willing to invest into a quartz-glass Toslink cable, optical is terrible and should be avoided.
4. DSD sounds better than PCM, *** IF *** you get a DAC with an I2S port and feed it with a USB-I2S bridge. If you go with a Schiit DACs, for example, you cut yourself off from DSD forever. The Teac I mentioned above can take DSD, although no I2S port. Oversampling your music to DSD 256 or 128 in your media player and streaming that into a DAC's I2S port will result in a major audio improvement.
Since you're interested in learning I'll offer a bunch of extra information to consider as you decide whether to pursue an amp or not rather than just recommending my favorites.
" i know these dont need an amp" should read "someone told me I don't need an additional amp and I fell for it" but I'll settle for "the amp I'm already driving these with is sufficient." You are already using some type of amplifier or you wouldn't be getting any sound at all.
What are you already driving them with? If you're already using a dedicated headphone amp, you're probably fine. If not, you are not getting out of your headphones what you could be. The dedicated amp has very little to do with volume, but everything to do with the details in the sound. The weak amps embedded in computers or mobile devices, unless we're talking a high end DAP, cannot achieve the level of detail or clarity or impact of a dedicated headphone amplifier (DAC considerations aside). Chiefest among the traits of a good amp might be the ability to provide actual silence when it's supposed to be there.
You should also consider your source. If you're listening to a highly compressed audio source, the dedicated amp will do little to improve your sound. Less than 320kbps will still sound like it's smashed into a can regardless of your amplifier (I'm lookin' at you iTunes). 320kbps still sounds compressed, but in my opinion it's not irredeemably bad and the convenience outweighs the negatives. YMMV though.
In that same vein if you're not listening to something with a high enough sample rate that your DAC can't support it you don't really need a dedicated DAC. If your source is typically a streaming service, your built in DAC is going to be sufficient for your demands and I'd just get the dedicated amp. If you're planning to use 96/24 or higher lossless files you need a better DAC to get the most out of them. There are still arguments to be made about the power supply improvements you'll find on a free standing DAC unit though.
Hope that's enough information to get you started.
Ones i've been looking at:
https://schiit.com/products/magni-2
https://www.amazon.com/FiiO-E10-USB-Headphone-Amplifier/dp/B005VO7LG6