In the spirit of "what can I do for a little money", I tried the following system out.
1. thinkpad X220 running freebsd 14.4
2. CX31993 DA06 dac
3. Douk audio U3 headphone amp
https://www.hifireport.com/douk-audio-u3-review/
4. Beyerdynamic DT-990 PRO headphones
5. 2-RCA to 3.5 mm jack cable (free, had one lying around)
If we ignore the price of the thinkpad, checking the current prices gives:-
CX31993 - 5 pounds (aliexpress)
Douk U3 amp - 25 pounds (aliexpress)
DT-990's - 135 pounds (amazon)
total - 165 pounds
Substituting HD560S headphones for the DT990's reduces the total price to 130 pounds.
Substituting a JM20 for the CX31339 adds 10 pounds to the total.
How does it sound? Not too bad. The amplifier has plenty of power to drive these headphones, it's plenty loud enough. However after listening for half an hour, I think the weak point is the U3 headphone amp, which gets a bit harsh and fatiguing after a while, depending on the type of music being listened to. So I would choose a better headphone amp if possible, if going this route, and spend a little more on the headphone amp itself. Perhaps the HD560S would sound a little more relaxing, the DT990's do tend to be quite revealing.
The little U3 actually looks quite well made, it has an all metal case and the volume pot and connectors all seem fine, you even get a power button on the back. I haven't taken mine apart but there are plenty of photos of the PCB online if you search for them. Certainly the exterior build of this small amplifier impressed me much more than that of the Fiio K11 R2R dac. I noticed on aliexpress that there is a 'pro' version of this amplifier for a bit more money, so that may be worth investigating. The sound quality is obviously not as good as a better grade amp like the Firestone, but really its pretty good for the price. Just don't pay too much, I noticed some online sites are selling these for a lot more than the aliexpress price.
Alternatively, you could just buy a JM20-MAX or JM98-MAX dongle and drive the headphones directly, and it will probably sound at least as good, for about the same money; although you lose the analog volume control and the flexibility of having a separate headphone amp.
Still, this exercise gives you an idea of what is achievable for not a lot of money. Personally I would not skimp on the headphones themselves, cheap headphones are a waste of money. The HD560S is another good choice, for a bit less than the DT990's, but I wouldn't go much lower down the range than that.
For a cost comparison, buying the DT-990's and the Fiio K11 R2R will cost 135 for the headphones and 150 for the Fiio, so 285 pounds total. That's using the K11's built-in headphone amp. If you then want to buy a better amp and power supply and use the K11 purely as a dac, you can probably raise that to 500 or more. Of course that's if you are buying new kit, ebay is always worth a look.