Im going to be the rebel here and probably get some critism. You do live in Arizona. Depending on the time of year and the environment your going to be backpacking, there are a lot of things you probably wont need. Rain gear comes to mind , tents come to mind. I would go with the blue sleeping pads ,again depending on season and area (desert or mountain) you more than likely wont have to worry about rain .

I would put the money into a quality nice fitting pack, Deuter is nice , REI brand also has a nice pack for kids. I live in SoCal and when I was a kid backpacking here in the local mountains we backpacked alot with next to nothing.

You'll need a stove, there are some good canister stoves for about 40 bucks .he snow peak and Msr have nice stoves for that price.

The rest of the stuff you can use your imagination, for example back in the day before the light weight cooking gear, we used to use metal coffee cans to cook with (boil water etc). You just need to use your imagination.

When I return from the sandbox in 6 mos, I plan on taking my family to JT for a nice trip. I was going to find a fancy tarp, I had one all picked out, But I remembered I have a good tarp, though not fancy , new or lightweight but I own it and it will work fine for a party of 5. I was going to use that as a ground cloth for us to sleep on.

So basically where your at right now I would buy the best you can afford, But you dont have to buy everything at once, Buy what you can/ really need, improvise the rest.

Check the Pennysaver, Garage sales, 2nd hand stores, recycler, there are plenty of places to get what you need if your on a budget.

Be creative and it will be alright