When I was doing Physical Therapy for my back injury and knee, they gave me some elastic bands to work out with. You can get them in any sporting goods department. They come in different colors for different intensities, from very mild to very hard to stretch.
I was told to start with just using cans of soup for resistance, then work up to the bands and slowly increase the resistance when it became too easy to do the exercises.
You have the right idea; just don't blow your budget unnecessarily on gym workout machines. If we were closer, I would go hiking with you. I start with an empty backpack, then slowly add weight to it for a similar distance, or just go a longer distance. Fresh air, sunshine, and exercise do wonders for mind and body.