Very new to high end audio - Recomendations

log out, google audiogon and when the site shows up select speakers instead of discussions.

The studio monitors are gears toward near field listening (as in sitting at a desk or mixing board) and are very flat tonally. 
Lots of people want more color (more bass, less highs etc) than flat studio sounds. Me I like a flat sound. 
Many (maybe most) powered speakers are geared toward the pro market abs designed just to hook up to a dac or preamp which your DAP could function as. The output voltage could be pretty low though as home equipment is designed for 3v input I think and protectable stuff is around 1.5v output. 
Power speakers designed for home a lot of times you can just use airplay or wifi from your phone. No “source” needed. 
Way our of your budget but something like Kef would be nice. https://us.kef.com/digital-hifi/active-desktop/ls50-wireless-2.html

Based on your audeze headphones (I have owned the LCDX) you might like the paradigm Shift A2. They have really strong bass for their size and soft highs. They are $350 each in the US. They have no wirless capability. 
https://www.paradigm.com/en/powered/a2

audeze have very strong deep bass. You will probably end up wanting a sub in the long run to be happy. 

I'm not sure how fussed for wireless I am. Not sure if spending the extra money for wireless if it's not going to be used. Isn't wireless quite limited with signal capability and high Res files?

Typically powered speakers are used in pro sound applications whether they be studio or live sound from a band. With your budget an integrated amp with a couple speakers would be the way to go. You can use bookshelf or monitor speakers if your room is not very big,. The integrated amp consists of a preamp which accepts the signal from your source ( CD player, streamer, etc) and sends the signal to the amp which sends the amplified signal to the speakers.
The integrated amp will give you the proper inputs for whatever source you use which is often lacking in powered speakers.

 Also Audiogon is probably not the best place to shop for you at this point in time. Most of the stuff will probably be above your budget. But have a look anyway.  Look at Audio Advisors and maybe  Crutchfield which will probably be able to put together a system that meets your needs at your budget. Also,  They have salesmen which may be able to help you with a phone call if that is possible for you. I believe you may be in Europe somewhere and I'm not sure the possibilities.

Hope this helps.

You might want to further your research at what’s best forum. They have many members who seem to have high end equipment and there are also speaker and audio brand sub forums.