I own quite a few higher end cans. LCD 2s recently came to my door, quite a few higher end Grados, sen 555,600,650, ext... ext...
To this day, my favorite jam out cans are still my d2k's. Even compared to their higher-price brethren, which I have listened to quite a bit, I still pick them just about everytime I sit down. They are just so fun and easy to listen to.
Now onto amping.....
I've had the 2k's quite a while, and thus they have seen a dozen or so desktop amps, and 5-6 portables. The best amp I have heard them on is my recently bought M^3 with o11 psu. Dont ask me to tell you why, but it really shines with them, even compared to some other amps (such as the little dot 1+) which are touted as great for low impedence headphones. Probly a little too much for a new guy though.
I tried them out of a E10 and they sounded just fine. If you wanted to spend a little more in the future, the little dots do indeed sound good and can be picked up used for a nice price in the sale section once and a while.
Cant comment about the burn in. I dont think I can remember that far back.
All the best,
Cory