Go the M50 route. The M50s are looked upon as sort of a first step into expensive headphones. As for an amp, you could live without one, as they can be driven by most devices just fine. An amp can make the sound a bit better, give it a bit of oomph, however don't expect miracles. If I were to choose between my M50's and my HD25's, I'd probably pick the M50's to be honest. The M30's is a step down from that.
It's thick, and I'm uncertain it would fit through a phone case (it probably would with some cases, but others not) - your best option to answer that question is to go down to a shop and try it out. If you can't try it, try to find a pair of HD25-1 II or some of the older Denon DX000 series and try them. The 3.5 mm to 6.3 mm jack adapter is interchangable among the three, so I'm guessing the thickness is about the same. Actually, I suspect most headphones have the same thickness to the screw part on the jack, so if you see threaded jacks, it's probably the same size as the M50. This is what my HD25-1 II threaded jack looks like, and how the M50's threaded part of the jack looks like:
All my cases are open at the top and bottom (for ease of use with docks and headphone jacks), so I can't try it out on one of my own, sorry. Hope it helped a little.