That's about the same distance as me, we fall into the grey area between being able to cycle in your work clothes if done slowly or going quickly and showering/changing at work. I chose the former and do 8 miles in an hour on the way into work (in my suit) then change and do the return journey in half the time
The one tip I have is get a pannier if you have to carry anything in with you, using a backpack = a very sweaty back!
It gets easier very quickly, when I started out I was a bit of a state when I arrived at work but two weeks in and you couldn't tell I had cycled.
I'd also recommend (not essential but I think you'd find it easier) swapping the mtb for a hybrid or tourer-esque roadie. Maybe a cyclocross (with gatorskins for the commute) would work if you wanted to use it off road too?