If you are on a budget (who isn't?), the easiest way to get started is to keep your single speed and find a couple of older mountain bikes... best ones to choose are steel and have rigid forks. Deore/LX/XT or if older STX-RC would be what I would look for concerning groupset.

Necessary gearing will vastly depend upon loaded weight, terrain, and your strength. The MTB gearing (probably 22/32/42 or 44 with 32T cog) should do it. Pretty easy to change if you need to go down a couple of teeth up front or change cassette.

As for you being the stronger rider... I'm sure she won't mind you carrying the tent and some the other gear as a equalizer.