If you don't mind new or used gear theres some great amps in this price range...
Bottlehead Crack (used)
darkvoice, la Figaro 337/339 (used)
Earmax original or The Pro version (latter used)
Woo Audio 3 (used)
Schitt LYR / 2 (new)
Little Dot 2/3/4 (new)
Darkvoice, La figaro 336SE (new)
I'm really happy with my 337 paired with my HD650. The 337 or its stable mate 339 would be my recommendation. Paper-oil audio caps, dual monoblock topography that uses dual triode 6as7G/6080 tubes with paralleled output to the headphones... no one else offers this in your price range (used).
IMHO the DV/LF 336SE also deserves a mention, don't let its price fool you... its a real over-achiever IMHO. I am just a big fan of 6as7G / 6080 tubes and paper-oil audio coupling capacitors (shrug). On that note you should also factor in additional $$$ to tube roll. The tubes can be more expensive than the whole amp!!
All of these OTL amps work great with the HD600/650, and I am 99% certain their engineers used these headphones to develop their designs.
Of the bunch the DV/LF 339, and the Earmax Pro are the only ones designed for lower impedance loads... if you ever plan on going that route. On that note every once in a long while someone on the BST board offers up a mad Ear+ for ~$550. Great amp for both high and low impedance loads, and its the only one on this list thats output transformer coupled.
Good Luck!!!
Oh welcome to HF and sorry about the wallet