Camping facilities in Yellowstone and Grand Teton in July

I'm going to be visiting eastern Idaho for work in July. I'd like to take the time at the weekends to visit the National Parks of western Wyoming - Yellowstone and Grand Teton. As it's pretty high tourist season, a lot of the accommodation appears to already be booked over the weekends, or where available, very expensive. It occurred to me that I could probably find a store to buy a cheap tent and stay at the camp grounds. My question is how practical/money saving will this be.

I'm flying out to the US, so I can't really take much gear with me (and aside from some tools and a sleeping bag, don't have much). So I'm likely just to have my clothes, wash stuff, a tent, a sleeping bag and a car.

Is this going to be sufficient?

I'd rather not have to buy cooking gear, so will there be other opportunities near the major campsites for food?

As someone who's never spent time in bear country, are there precautions you need to take against bears even at the tourist (as opposed to backcountry) campsites?

How practical (if you just need a small spot, no hookups) is it to just arrive in July and expect a pitch to be available?

I can see from the National Park websites which sites have washing facilities etc, but it's hard to judge how suitable (or not) each is for the poorly equipped visitor.