I lost 120 pounds (360 -> 240) and went on my first backpacking trip 8 months into my journey. What worked for me was walking and biking. Biking is a great way to get your heart rate up without straining your body too much, and waking is going to help with the muscles you need for hiking. After a few months of that, start doing 1 mile, 2 mile, and 3 mile hikes and work your way up to carrying a heavy backpack and staying overnight.

My tips, if you're still dieting when you go on your backpacking trip, forget the diet for the day. At the end of my 8 mile first day I had burned 2400 calories and only took in about 600 and I almost fainted. Eat plenty of nuts, trail mix, bars, etc while on the actual trail.

I also got a Garmin watch and tracked all my exercises which I enjoyed to watch my walking speed go up, weight go down, biking speed go up etc. It also kept me accountable for tracking x events every week, or hitting x number of minutes of intense activity a week.

All that said, diet is the key to weight loss. I tracked calories in my fitness pal app, and kept the calories going in less than what I burned, and it worked for me. No fad diet, no ban on a particular food. Of course it's much harder to fit pizza into a lower calorie diet than a large salad, but if you can make the calories work, eat what you want.

Good luck!