Need new headphone setup.


I have a speaker oriented system that is very satisfying to me. But because of a need to maintain domestic tranquility I’m looking to go to a less noisy alternative: i..e. headphones.
I want to spend a total of about $1000. So, nothing too fancy. Not the equivalent of my much more expensive speaker system.
What do I need to assemble a headphone system independent of my regular system which is accessible from my listening chair and side table?
I plan on solely streaming. My present system contains a WiFi streamer.
Can that be incorporated, or do I need a new streamer?
I understand that I need a headphone preamp along with the cans.
I know my budget is not too high, but can I get something relatively decent at it?

Currently, I listen though cheap ear buds and stream through an iPad.

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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.

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. 

You might consider the Austin Audio Works Black AMP.  It was on a SBFA tour as a good a great headphone amplifier - no feed back current mode when used with the Audeze LC series of headphones is a most rewarding combination of detail and clarity.