How do you try out headphones?
What should you be looking for besides comfort?
What are some common ways that sound you hear may differ from what you would expect from a frequency response graph?
Besides listening to a sine wave and your use case what else should you test?
The only earphone I've tried and found offensive was the Tin Hifi t2 as the treble/sibilance was painful.
Some MP3's are touchscreen input without volume or sound buttons. I'm excluding those.
It's not all that easy to try them out and sometimes ain't possible to do so. If you have developed preference you read about it from someone who has a similar preference along with measurements. You look for; fit, comfort, seal, low distortion, sensitivity, build quality and of course FR. Main thing is that highs are alright and nothing is to much of from what you desire in the first place.
Distortion, enclosure refractions.
I don't listen to tone generator or white noise, I might if I feel something is really off. I listen to material (music) that I know wery good for various aspects and again if I subjectively feel something is off to test it. You should test response to EQ and use EQ to improve response of course. Sometimes even small variation in FR can sound very different for bad and good like mid bass boost as example of a bad one. Didn't find Tin T2 offensive bright, bit in front, tiny, definitely bass shy but not bad with EQ... Definitely not a best sounding IEM's but very strong build and good for recreation where you expect them to hit the floor from time to time.
Back to beginning in this time and age a lower or mid tire Android phone (Qualcomm SoC based) with 3.5 mm out and SD card support paird with good software like Hiby Music / Wavelet and 16~32 Ohms sensitive (115 or more dB/V where 0.5 V is plenty) earphones/headphones will do the job very good and on the long run. Of course you still won't have a replaceable battery but you can pick a brand where such thing is easier to do (iFix-it based).
Even basic Samsung IEM's that come with the phones or old Sony MH755's with EQ sound pretty nice and that's in cuple bucks category. So in short if you didn't use EQ start to do it and have reason not to demand something unrealistic (open back's with harman bass or pushing sub bass from those that can't do it) and you will be fine. I genuinely don't use IEM's on the long run, sometimes when I do work outside with loud machines I do and that's about it. On the go my favourites still are Creative aurvana Air earbuds for surrounding awareness especially in summer time, have a Denon AH-D5200 headphones as last purchase which are OK when I have to use headphones in the first place. It's safe to say this day's I am pretty much speakers guy (80% of time) and a bit lucky that I can do that (deticated room sound isolated from the rest of the house and good and not too many neighbours). Tho a bit compulsive - obsessive when it comes to DSP (not that I like to do it often, just comprehensive and to the end).
Automatic headphone equalization
autoeq.app