I second the recommendation for a Black Ice FX Tube DAC. I have this DAC and like it very much but it is not my primary DAC. It did very well in a blind shootout at the Arizona Audio/Video Club DAC Shootout and I have had good experience over the years with equipment designed by Jim Fosgate.
I have two other DACs - a Berkeley Audio Reference 2 MQA and an Audio Mirror Tubadour IV. I also have a Marantz KI Ruby SACD player. Before these DACs/Players I had a PSA PerfectWave MK II and a Marantz SA 8005 SACD player.
The main point I would like to make is that in my experience there just isn't a lot of difference between modern DACs in how they sound. If you do a careful A/B comparison with matched volumes you will probably find that you are hard pressed to tell one from the other. If you are after a certain "sound" a DAC probably isn't the place to find it. It's nothing like changing phono cartridges, for example. One might think that my Berkeley Audio Reference 2 would blow away the other DACs but I have to admit that the differences are very subtle. I found this unit for a very good price used and I have a collection of HDCDs which it will decode but it certainly doesn't sound 20 times better than my Black Ice. Having the Berkeley gives me the satisfaction of listening to a DAC that is considered as one of the best and I don't think I'll need to upgrade again. If I wasn't so OCD about my stereo the Black Ice would have served me very well for the rest of my days. I got the Tubadour because I wanted to try a NOS DAC to see what the hoopla is all about. It's still breaking in but it also sounds pretty darn similar to every other DAC I've had.
The reason I recommend the Black Ice is that it's well within your budget and at least you can try different tubes which gives you some ability to modify the sound. Otherwise I suggest that you select a DAC that has the features you want, a story you connect with, and gives you the best pride of ownership. Then sit back and enjoy the music.