Lots of alternatives..With prices all over the place...Let alone closed vs. open, dynamic vs. planar..
So, thinking of ' a journey of 1000 miles starts with the first step', why not buy something inexpensive but well-reviewed, listen to it for a bit, deciding what you like and don't like - then 'upgrade' (if even necessary) from there?
First, open vs. closed. With one exception (the AKG N90Q) I have never found a closed HP I liked. Hot, sticky (to me) , after an hour or so. I do have the AKG K371. Rarely use it, but for $149, if you must have closed, why not start there?
Now open For $149, you cannot beat the HE400se. Forget the HE400i (2016). Again, I have both. With the 400se 'stealth', there is no reason to consider the 400i, ever.
Amp - Magni IE at $139? Don't have one - but you like it - looks good - why not?
Now the DAC...and something you won't be expecting...a $109 Qudelix 5k. Yes, Amir basically panned it's DAC, but it's SINAD is still 90db down. Plenty sufficient. And you get it's great PEQ functionality, letting you optimize various HP FR to your taste. (And yes. I have this, too. It's the DAC in my own 'everyday' HE400se system). Use it front ending the Magni IE. Or you 'could' defer the IE and use it Balanced with the HE400se (w/$42 or so cable, unfortunately).
A place to start - $150 for HP, $109 for DAC/Qudelix, $139 for Amp (or $42 for balanced Qudelix cable)..Listen a bit. PEQ a bit..go from there..