Right now I'm deciding what I am going to do regarding an amp/DAC stack and whether the right streamer or DAP will help in producing the best listening experience.
A DAP or dedicated streamer will def be an improvement over a general purpose computer or laptop as a source.
Hearing about others experience with finding truly magical moments with the proper synergy in their setup, makes me want to do it right from the outset.
I think all of us felt the same way when we first got into this hobby, but I can count on zero fingers how many of us actually achieved game over status after the first major shopping spree.
I think it's important to understand that this hobby is more about the journey rather than the destination. Along the way, personal tastes evolve, new headphones come out, new amps and DACs too and then before you know it, what you thought was your own personal audio nirvana suddenly gets turned on its head by a new or different sound that makes you sit back and realize how much you've been missing out on.
Budget wise I'm will to spend upwards of $4k, all the while being mindful of diminishing returns.
I like a more warm, musical sound and am not looking for something overly analytical or sterile/clinical sounding.
The Law of Diminishing returns is very real within this hobby and it's good that you know this from the get go.
A couple pointers to get you started on your quest for a warm, musical sound...as I have the same preference.
DACs:
Generally speaking, a R2R DAC or a tube based DAC would most likely be where you'd want to begin your search. Delta Sigma DACs tend to sound cleaner, with sharper leading edges often come off as having better detail retrieval, whereas R2R DACs have a more rounded, warmer, smoother, more analog sound.
Now, that being said, not all DACs follow this rule. Some R2R DACs lean into a cleaner sound and some lean into the warmer side of things. The same goes for D/S DACs.
Amps: Again, generally speaking, tube amps tend to be where you will find that warm, lush, musical experience. There are lots of different tube amp designs out there: OTL, TC, SET, tube hybrid. In my experience the king of those designs for a warm, floaty, holographic sound would be an OTL amp. Unfortunately OTL amps only work well with high impedance headphones. The headphone you purchased is a low impedance/high sensitivity headphone and will sound like arse from an OTL amp.
For your headphone, you will want to focus on TC or SET or even a tube hybrid amp. I have much less experience with these amps than I do with OTLs, but from the ones I've tried, it's a very different sound. Again, cleaner, faster sound with less tube flavor than an OTL.
Regardless of which design you go with, the tubes themselves can play a massive role in the presentation you will hear. Tubes are a major rabbit hole and not a cheap rabbit hole either. It's not unusual to have as much cash invested into the tubes as you have invested into the amp itself.
When buying a new tube amp, they typically ship with very cheap, readily available, modern made and poor sounding tubes, typically of Chinese or Russian origin. The magic of tubes comes from NOS(New Old Stock) tubes, some of which that date back to before World War 2. Of course there is a very finite amount of tubes from the 30s-50s available, and everytime a pair of these tubes are sold, that's one less pair available for the rest of us, hence the often times ridiculous prices NOS tubes command.
Which brings me to my next point: research the prices of tubes prior to buying a tube amp. Not all tube amps use the same tube types. Some tube amps use esoteric tube types, of which there isn't a massive demand. Then there are other tube types, like 300B, 6SN7, 5998, etc...those are ubiquitous in many amps. Wanna gag? Check the prices of Western Electric or Elrog 300b tubes. Check the prices of Tung Sol Black Glass Round Plate 6SN7s. Check the prices for a matched pair of NOS Tung Sol 5998s.
So, again make sure you know which tube types any given amp you are considering uses, and then check prices. Sure, a circa 1960s RCA 6SN7 will be much cheaper than the black glass round plate Tung Sol, and you will definetly hear the difference too.
Final piece of advice I can give on tube amps and tubes is just because you bought the most expensive tubes available doesn't necessarily mean you will enjoy what you hear. Tube rolling is like cooking. Add too much garlic powder to a dish and you will ruin it. One needs to experiment with various tube combinations in order to find your own personal happy place. Fivre 6J5+ Western Electric 421a+ GEC U52 might sound killer on one headphone and total garbage on another headphone. That's two grand USD worth of tubes, BTW.
Solid state amps: This is much simpler. The sound you buy is the sound you get. For a warm, musical sounding solid state amp, I'd suggest reading up on Violectric amps. The v222, v281(discontinued, but available if you know where to look) and to a lesser degree, the v550.
Another, potentially cheaper option for a warm solid state amp can be found by using vintage stereo receivers from the 1970s(don't laugh) Unfortunately those again sound their best with high impedance dynamic driver headphones. Your headphone will get a bad case of bass bloat due to impedance mismatch on an old receiver.
Again, this hobby is a journey. There is so much to consider, learn and discover along the way that it's virtually impossible to nail it the very first time. If you really want to skip the journey, buy your gear and never return to Head-Fi and hope that your audiophile nervosa doesn't kick in.