I frequently do this kind of conversion when someone needs an inexpensive but capable city, trail, or campus bike. I look for an mtb with a good rear derailleur, functioning brakes, wheels that won't have to be rebuilt, and hopefully a useful flat bar - to keep costs down. This bike I did is pretty typical. Go with tough street tires, replace shifters with one trigger shifter, remove front derailleur for simplicity if you don't need a climbing bike, add a chain guard if possible, put a hi-rise stem on to move the bars up.
Collect some hi-rise stems - they are very cheap. New trigger shifters are inexpensive and there are hundreds of 7-speed compatible derailleur bikes out there. Sram triggers for 9-10 are also cheap if that is what you end up with. Grab handfuls of MTB brake levers at the next swap as they are likely to be trashed on your donor bike. I really like to upgrade the crank if I can to a hollowtech or gxp because I don't have to hassle with bottom brackets and the owner won't have crank issues. 110 bcd is really flexible on a city/trail bike, works fine with a mtb front derailleur. And there are now plentiful 104 bcd hollowtech cranks out there if you need a 24 tooth ring.
