Newbie Requests Advice

Hi, my fiance and I are looking to start bike riding. Both of us biked around town some when we were in college (now 28-29). We haven't for several years for different reasons. We want to get back into it as a way of exercising. I am 5' 4" and 170 lbs. He is 6'3" and roughly 300 lbs. He has no major issues; I, however, was in a car accident a couple years back and have finally been approved to start doing whatever I want. I had rotator cuff, bicep tendon, and labral tear repairs. I also suffered from nerve damage in my neck, shoulder, and upper back. The majority of my everything has been fixed, however, I do still have some pains if i keep my neck in an outstretched low position (think marathon bike riders position). We are not sure where to start with picking out bicycles that aren't Walmart throw-away bikes. We still want to stay relatively cheap (max of about $500-600 combined). We would be riding mostly on city roads or gravel country roads. On occasion, they may do some riding in some mountains (if we get to that level of ability). Neither of us intend to become hard-core bikers. What are the best suggestions on what to buy, maybe things to make it easier, better suited? What things should we look for in a bike for someone on the heavier side? Truly, what advice/suggestions do you have in regards to literally anything for us. We intend to go to a local bike shop and talk to them, but I wanted some non-sales advice prior to going there. Thanks!