You don't need to spend a fortune to meet your mission. Main thing that you gain is better gearing with "better" being subjective. For 95% of road trail conditions, basic gearing will get the job done. Frames are frames (my own opinion only) and I am just as happy with my $300 Dahon as I am with my way more expensive Chameleon. For your 1st I would recommend what I affectionately would call a "beater" or entry bike, so $250-$500. The Dahon is fine on packed dirt and gravel. 20-inch wheels big enough to mostly keep you out of trouble. You might look for more than a 7,8,9 speed depending on those hills, but I did an event in Vermont that was almost all hills and the roads were all dirt. It hurt but I climbed every hill on a 7 speed. A few more gears would make life easier for you.
Things you should look for that I did not know or thing about for my 1st...adjustable stem/handlebars (I got lucky and it came with them), headset that supports a bag (Brompton adapter gives you Brompton carrying ability without the Brompton price), fenders- you will rejoice when you need them, kickstand...I using it when folding/unfolding and when having the Brompton bag on and loaded.