N.,
Ages might help here: Don't buy the junk. No idea how old your kids are - so I have no idea if they have access in other places. If it isn't in the house, they can't eat it there.
Limit TV (advertises junk), teen magazines (advertise junk), and put healthy alternatives in the fridge.
Even if you just put a veggie tray with dip (no double dipping! :) in there, they have that option, and a little ranch dressing is better than a bag of chips.
Airpop popcorn with oregano. It's incredible. (absolutely insane with butter, but you're trying to avoid that :)
Have 2 veggies and a bland starch - plain rice, and meat if you eat it.
Get different veggies, and try them out different ways. Low salt is a good plan to think about too. Find out what you like, and they will usually follow suit.
Fruits, too, would work for a tray.
Sadly, I qualify as a Mom, but not as a Mom with teenagers. I only know what I did when I was a kid - Mom didn't keep that stuff in the house - we couldn't afford it. 'We don't need that' was the mantra of the day. Didn't help me want things less though. I think if she had approached things differently, I might have different.
For exercise, I would not recommend a pet. You can't make them walk the pet - it would become a control issue too easily, and the pet might suffer. Exercise was something my Mom got me into by virtue of 'you're going to do something, not sit around the house reading all day'. So I was in soccer (didn't play well) and swimming (fared better, but not a passion that stayed with me).
What YOU get into with them might be the best course of action. Take them to the park, and they will get exercise as a by product, even if it is walking to the swings. Get into hiking and green paths (cleaning as you go - de-litterizing). There is so much you can do together.
I wish you luck,
M.