Replacing BB, but found mountain + road cranks and am confused
To use a 68/73mm bottom bracket in a 68mm bottom bracket shell, you use more spacers than the 73mm shell (normally 2 x 2.5mm spacers extra). Or in other words, you leave some spacers out when using it in a 73mm shell.

If you have a 68mm shell and road cranks, your best bet is to use a 68mm road BB. The dimensions are just a little different on the cups, as explored in this question here. The differences are slight so plenty of bikes could have a mountain HII bb with road cranks, normally without issue, but if you're wondering which to buy, I'd go with the proper road one.

Don't forget that creaks can come from lots of places, don't forget to check things like your headset, QR skewers if fitted, saddle rails etc.

If the threads were resisting, and you didn't put the wrong cup in the wrong side(!) then the threads in the frame may need 'chasing' with the proper tool. Doesn't take very long in the LBS if you don't have the tool (expensive). A clean thread typically accepts a new BB cup being threaded all the way in by hand. A rough thread however will feel tight and need some force. 

I like installing a BB into a cleaned thread, threaded by hand, so that I'm confident it is not cross-threaded.