Graham Slee Solo £445 8/10 with HD600
MF X-Can V2 £150 7/10 with HD600
Creek OBH 11 £129 6/10 with HD 600
Chiarra kit £209 9/10 with HD 600
B-Tech 928 £30 6/10 with HD600
MINT £50 6.5/10 with HD600
From my experience with these amps.
If you can DIY then the Chiarra may be the way to go but if you don't know one end of a soldering iron from the other then the MF X-can V2 cannot be overlooked at the budget end of the scale. If you've got £445 to spend on a commercially made amp then the Graham Slee Solo works particularly well with the HD600's.
The X-can V2 can be recapped and you can roll better valves into it to suit the HD600's but this costs money and is an ongoing thing!
If you're on a real tight budget then a MINT with a 24V power supply is up to the job....... if you're on a "really" tight budget the B-tech 928 is a good buy at £30 but only if you spend an additional £20 (or thereabouts) to replace the caps with ELNA silmics and swap the NE5532 op amp with a OPA 2107 and bypass the tone control. The "stock" B-tech is pretty dire
You can also look at the secondhand market and pick up a PPA, Sugden headmaster, Pimeta etc. etc. etc. for a good price.
It's best if you can audition the amp before you buy to ascertain if it's pleasurable to "your" ears...... forget the reviews here.... it's your ears that will be listening to the music. Use Head-Fi as a guideline to the amps that are available and nothing more...... your ears are the final judge.