K yama you're set dude.
Cheese, bread, milk, low fat foods really serve no purpose (besides tasting pretty good)
TO make the fastest progress possible you need to stay the hell away from ANY processed foods so it sounds like you will because you dont have a choice.
Stick to lean meats, vegetables and unfrefined carbohydrates. you may have to use rice as a stand in here which is fine but do the best you can to get brown rice... If you only have access to white rice we'll have to go another route.
If you can get Eggs, oats, meats, green vegetables, yams, and potatoes this is the best case scenario. Let me know what you have access too. Once I know what you can get your hands on regularly I'll give you some more specific tips.
You sound like you're in pretty good shape to start with, dont pay any mind to BMI its pointless as a health indicator. (im very biased because im well into the OBESE catagory)
As far as working out you have everything you need. Machines just make life easier thats all. you dont need them.
CHest: presses and flys
SHouldrs: military press and lateral raises
Back: Rows and Chins
Abs: (your lower back hurts because your abs are weak so start slow but try to progress) crunches then work up to leg raises and decline sit ups.***
Arms: Overhead Tricep ext and curls
Legs: Squats and Lunges (lunges suck but they will tighten you up better than anything)
Calves: standing calf raises w/ dumbell
has some great animations for these and tons more exercises .
*** when you do decline sit ups only go back so far that the tension doesn't transfer to your lower back. You'll feel it if you go to far down the lower back will suddenly take up all the work.