They normally give adapters with those types of cards. At least when I was still working in IT retail about a year ago, every card that came with a mini HDMI port came with an adapter. You can always check the box if it's a non-sealed box or ask staff from wherever you're buying it.
I would personally recommend aiming for a 760TI or better a 770 without really breaking the bank if you're planning on gaming a lot, the higher you go the better but the 750s are only just leaving entry level gaming cards. If you're not playing heavy stuff than a 750 is more than enough, even the GT series would suffice lol