Before you do anything load the Audyssey App. They have sound shaping that tweaks the output of your iPhone to get best sound from individual models of headphones, and earphones. It is not an graphic equalizer, but you can shade the sound tipping it either to the treble or bass side. I have run it on iPod Touches and iPads for years it is really good. when you set it up you go into it's device library and pick out and list what you are using earphones, headphones and the lists is extensive and getting larger all of the time as new stuff is being added.
The App:
http://www.amp.audyssey.com/
Here is what Audyssey does:
http://www.audyssey.com/
As for earphones with a mic there is nothing better the the Etymotic HF-3, $140.98 from Amazon, They have a very accurate sound are great especially when you are using the Audyssey App. It is my go to choice for my current Touch 5 and iPad Air. It also happens to be the best for passive noise reduction. And gets even better if you get them custom fitted by and audiologist.
http://www.etymotic.com/ephp/hf3.html