Headphone no cost limit.

STAX SR-009 with the right driver amp (usually tube or FET/Tube hybrid).

I use an old Stax SRM T1S driver amp, with NOS RCA clear top tubes.

STAX R&D uses a similar driver amp Today.

The driver amp makes a big difference, and only a few are real good.

Acceptable new driver amps are $2150 (STAX SRM 007TII) and up, to over $5000. Look at the Head-Fi website for more info.

SR-009’s are $4500 in the USA, and about $3500 direct from Japan.

Here’s a link to a site that covers headphones.

http://www.innerfidelity.com/frontpage

Click on the "Wall of Fame" link to see what the editor thinks of various headphones.

Best headphone?
Open or closed?
Dynamic, magnetic planar, or electrostatic?
Interface single-ended or balanced?
Power requirements, player type?

There’s a lot of variables to picking a headphone. It is also a growing hifi sector that has been bringing a lot of new technology to market.

Good luck in your search.

Best of them all , current in production.

Head-FI is the largest and best headphone site.
Biggest forum. Thousands of posts. Many reviews. World views from many experts.

Forget innerfidelity. It is one person’s opinion. He tries to measure and fails.

Like any ’BEST" post, YMMV, and IMO.

Read and think.

There are many choices at different price levels. I gave mine.

Best of them all, current in production, no cost limit.
Then put these on your list.

http://www.wired.com/2015/11/sennheiser-orpheus/