You might check if you can get a southwest flight. That might be the least expensive for you. I would definitely fly. Southwest flights are not available via the usual web sites, you need to go to their own web site,
www.southwest.com. Of course often the other airlines will match southwest fares, so this might not be necessary. But my experience is that it does not hurt to check them out.
Although you will need to rent a car wherever you end up.
Three ways you can go, Phoenix, Las Vegas, Albuquerque. Where you go and what you choose depends on what you want to do when you get there.
Phoenix is about four hours (?) south of the South Rim. If you come from Phoenix you have the option of driving via Sedona and red rock country. Also there are some great views from the highway between Phoenix and Flagstaff.
Las Vegas is closest to the canyon, and is the easiest to get to the canyon from (allegedly, I have never been there). I understand that the route, while the fastest is (arguably) the most boring.
Albuquerque is my choice, personally. From Albuquerque itself you are wighin distance to do things like Chaco Canyon, Taos, Four Cornerns, Monument Valley. Also the drive to the Canyon allows you to pass through the Navajo and Hopi REserrvation, the beautiful desert, and the Painted Forest. Stops at Window Rock, Canyon de Chelley, the Hopi REservation, Tuba City and Cameron are all worthwhile. This is, however, the longest drive, it will take you at least 8 hours to do it. Again, I think it is the most interesting choice, but will tkae a lot of time. If you do it in 8 hours (it could be longer) you cheat yourself. We took a couple of days, stopping and riding horses in Canyon de Chelley, visiting Window Rock (staying at the Navajo Nation INn) and such.
FWIW
Julie
P.S. This is a very opinionated post. y