open headphones will have the widest soundstages and the best positional audio however leak sound both in and out. if you have very loud ambient noise you might hear that inside open headphones where closed headphones would drown most of that out. if the ambient noise level is above 40-50db then open cans likely will be a bad idea, if at that level then you might be okay but may hear some noise, if below you should be completely fine. db chart example
http/alexandriava.gov/uploadedImages/tes/info/typicalsoundlevelscr.jpg
you should use an amplifier with them but the dt770 are good closed headphones. for closed cans they have surprisingly good soundstaging, good clear bright treble and good bass. they are v-shaped in profile so mids will sound a little recessed but that generally makes them sound exciting. comfort is well known to be good even for people with glasses.
if you're a basshead ultrasone 580's or 780's arent bad. the denon d1100 have good bass and decent quality although build quality is questionable.
the m50/m50x are also not bad... if you can pick them up for around $100-130. similar to dt770 but inferior in all points. soundstaging is also very bad - all sounds will sound very close to you. i personally own a pair and do like them but i'm just being honest with the specs. a good choice if you can get them for a fair price as they have good quality although not so ideal for gaming due to soundstaging (though you can certainly use them).
as for microphones... look at the modmic, moovmic (slightly less quality), lavalier mics with an adapter (can range in quality from better to fair), zalman clip on (you get what you pay for but its cheap), or desktop microphones like the snowball.