Flagstaff is only 260 miles (4 hours) from Tucson. The south rim of the Grand Canyon is 350 miles (5.5 hours) from Tucson. Paige is 400 miles (6 hours) from Tucson. This makes it an easy drive from Tucson (to the south rim anyway).
There is a non-refundable fee of $10 per permit plus $5 per person per night camped below the rim and $5 per group per night camped above the rim. Frequent users may wish to purchase a one-year Frequent Hiker membership for $25 that waives the initial $10 fee for each permit obtained by the trip leader for twelve months from the date of purchase.It is not clear just what the "quota" situation is from the website, but it does seem clear that there is competition for opportunities and some kind of use limits, so they encourage applying for permits by mail with alternate dates and routes and all that.
There are only 30 miles of maintained trails, everything else is what I would call "adventure hiking" and can get quite serious.
Heat and the need for water dominate the planning of any Grand Canyon hike. It is also important to remember that you will often begin a hike in the cool of the morning and have an easy time going downhill, then will find yourself hiking uphill in the afternoon heat. This gets lots of people into trouble.
It is sometimes said that Grand Canyon hikes are best avoided during 5 months of the year. From mid-May to mid October heat is almost guaranteed to be a serious issue. This conflicts with most peoples summer vacation schedule, which leads people to attempt hikes in July when heat is most extreme. This is a time to be up at 10,000 feet in the mountains of Colorado or California, not in the Canyon. Since I live in Tucson, I have the chance on any given day to sample heat similar to the Canyon by hiking in the desert where I live. Due to the oven like effect of being in the Canyon, I expect Canyon conditions to be hotter than Tucson. A person from another part of the country, standing in cool conditions on the Canyon rim can easily be deceived about the conditions below.
Harvey Butchart was the great explorer of the Grand Canyon. There is a biography "Grand Obsession: Harvey Butchart and the Exploration of the Grand Canyon" that is highly recommended.
I have some notes on Harvey Butchart as well as some of his hiking logs in a separate section here.
And I have a local copy on my home machine. (This link doesn't work, even for me.)
The Grand Canyon Treks website has a lot of interesting material. In particular it has a list of water sources.
There is a book "On Foot in the Grand Canyon" by Sharon Spangler. Her life is a peculiar story (she was murdered by her psycho-killer husband Bob).
The book "Death in Grand Canyon" should be considered required reading. It is much more positive and informational than you would expect.
Tom's hiking pages / tom@mmto.org