Need new headphone setup.

Good luck with your HD600 and Cobalt!

I was gonna say that the Cobalt is great. I use a Black myself but has listened to the Cobalt in a store and it is better.

If you ever want better headphones I suggest trying Focal. I think the Elex from Drop is available for $700, cheaper if you buy used. I have Beyerdynamics Amiron Home which were said to be slightly better than HD600. There is also DT1990.

You can also look around in the headphone forums for more ideas once you get hooked. For example in Reddit. 

I'm sorry, but all "ear speakers" absolutely do not sound fine if they are used with "top shelf" components feeding them. If that were the case, then the same would be true for typical home speakers and that's clearly not accurate at all. As for the OP, you do not need a headphone preamp at all. You can use some preamps as headphone amps if they have a jack, but you don't need a preamp for a headphone amp, if that's what your asking.

Can they be open headphones which leak sound or do they need to be fully closed?

If you can use an open set then consider the HiFiman Ananda with the Topping DX3 Pro+ amp/DAC/Bluetooth combo.

For a closed headphone, there are not a lot of great choices.

Get HD560S, better bass that HD600.

also this combo is a killer.

Topping E50 DAC + L50 combo.

TOPPING E50 DAC + L30 Headphone Amplifier + RCA Cable Combo (shenzhenaudio.com)

Regards,

I recommend the Graham Slee Novo headphone amp and a pair of Shure 1540 headphones...right at your thousand buck budget. I think you will be happy with both. The Shure's are closed back but with an open back sound. Another option is the AKG K550's, also closed back with an open back sound.