I'm not known for being brief so my apologies. Take all of none of this advice because it's worth exactly what you paid for it!
I would skip running unless your weight isn't an issue. Being overweight (not saying you are!) and out of shape going straight to running could cause knee issues and spoil the trip.
You can get as complex or simple with both training and diet as you want.
If the desire is to lose weight, max incline treadmill for an hour. I would also advise weights to give you some high intensity portion of fitness. Treadmill first thing in the morning before eating is a popular approach and then do a weigh routine in the afternoon. I would skip squats and free weights unless you are confident you have good form. Leg Blasters could be a great option (Try to start with 10 minis. After you do 10 minis, do 1 full then 9 minis, working towards 5 fulls)
Half of a full Leg Blaster 10x Air Squats 5x Lunges -each leg 5x Jumping Lunges- each leg 5x Jump Squats Performed as quickly as possible one exercise immediately after the other.
mtntactical.com
While legs and core would be your focus, you can't life legs every day. Work upper body and back as well. Having overall fitness won't hurt.
For diet, figure out you caloric needs and your weight goal and then adjust. I think a food scale is the most beneficial facet of diet. 6 oz of rice may look a lot different than you thought and portion control will help substantially. Once you figure out the nutrient breakdown you can quickly figure out a rule of thumb for meals (e.g. 8 oz protein 6 oz carb)
I hope to hear more about your fitness progress and your thoughts after the trip!