HD 558

Sennheiser HD 558 and Rihanna. The clarity and impactful bass was just off the charts for my first real solid open headphones.

Similarly went with a 558 almost fifteen years ago now. Kinda miss them still. 

I consider discontinued HD330 (later HD465 I think) as the best on-ears I've heard, but they are pain to refurbish - no direct replacement for earpads or rubber/silicone headband strap (straps can still be in good condition though). There is a higher model HD340 / HD475 which I haven't tried, nor anything Grado. I consider the above to be better than 60Ohm Koss (not a comparison really), or the very popular HD480 Classic II, or some more current lower-mid level over-ears like HD559, but not as good as say HD555/558/579. I might pick them over HD599 though, just because I don't like the bloated tonality of HD599. So all in all, it is still not the level of hundreds of dollars, but very usable.

You don't really have to worry about impedance unless you would want to use some super low impedance IEMs. I've checked the spec, but I can't find power output of your player, that is a weird thing to omit when they output impedance and even IMD listed. Since it is based on CS43198, it should be able to get 2Vrms from unbalanced and 4Vrms from balanced into high impedance loads, but if there is more or what is the output into low impedance is unknown. Given the price of the device I would mail/call their support and demand exact information about output power. Anyway if the 250Ohm recommendation you got was DT770/880/990 then, that would not be a very good one as those headphones work only with unbalanced connection and their 250Ohm variant needs 2.5Vrms to reach 110dB SPL (loudness). So among Beyerdynamics models an 80Ohm variants (so only DT770/990, as there is no 80Ohm DT880) would be much better pick since they only require 1.4Vrms for that. You should be fine with anything from Sennheiser from 500 series, so HD560S/505/550, including possibly HD58X from american Drop store, and also HD490 Pro. I would not recommend going for 600 series which will work fine, but in their case I would advise getting balanced cable for those and if balanced output in your player is limited to 4Vrms, I would say 600 series can get better with more. Aside those you might want to take a look at planars like FiiO FT1 Pro and Hifiman headphones, but I do lack experience with those so can't tell much. Spec wise FT1 Pro should run fine even from 3.5mm unbalanced, while Hifimans can vary a lot depending on the exact model. Be warned though, Hifiman is kind of known for poor reliability (but also for not making problems with warranty claims and just replacing faulty units).

The Sennheiser brand was sold off a long time ago, and nothing good has come of it since the HD558. It depends entirely on the product, but it's always the same rubbish.

The jump from apple earpods (the ones that came with the ipod nano) to Bose QC25s was insane. From bose qc25 to HD558 was even crazier. From hd558 to hd660s2 was less noticeable, but still there. Above $500 the price/performance falls off a cliff. You’re mainly paying for high-end materials and handbuilt quality above that price point.

I have the HD558 model. They've seen a lot of use, but it's so easy tos replace worn parts.. I've replaced the cord, replaced the ear cushions. They are connected to my Marantz NR-1603. I wish I had DTS Headphone:X (the pre mixed track on Crimson Peak sounds great), but funnily enough, most reciever manufacturers don't stress their headphone capabilities.

HD558 on the budget used side, otherwise 560S or HD599.