AKG K553 MkII

If you want the most for your hard earned money, don't go wireless. Feel free to check out the Sony MDR-M1, Austrian Audio Hi-X60, Sennheiser HD620S (tip: manufacturer refurbished directly from Sennheiser), Fiio FT1, AKG K553 MkII, for example.

AKG K553 MkII (Music Store Köln (Cologne) Germany €139, for example) - detailed, quite spacious sound for closed headphones

Feel free to check out the AKG K553 MkII, for example. 👍🏻

Also very nice but not specifically bassy: the AKG K553 MkII.

next best after that would be beyerdynamic dt700 pro x and akg k553 mkII

you can usually find akg k553 mkII on sale for less money and that's just as good as 700 pro x if you want closed back

for immersion you would probably want some bass too so best options would be ... 700 pro x or akg k553 mkII for closed back in your price range

you can probably get AKG K553 MKII on sale maybe Beyerdynamic DT 700 Pro X too, they are $240 and $250 msrp, both have great build quality