I thought you wanted cheap? With doing all that you are buying a lot of stuff and may fit larger than 31". If you want to do all that, don't... and just do a spoa. I think Wrangler springs are what everyone is using. It can be done cheaper than all that other stuff. I've got a 3" body and 3-4 custom springs and shackles, but you can do things easier and cheaper than I did. I'm running 33's. If you do replace the shackles make sure you use ones with a reinforced center. They should look like an "H".
And yes, any tinkering with the springs/suspension will require longer shocks. That is why I recommended a body lift. No longer shocks needed for them. A plus is the helps keep the center of gravity lower. If you tell us how much $ you have to deal with it would help. Can you weld? Be ready to trim some bumpers and such.
Do you have your heart set on 31"? They will give a little harder ride than a "P" size tire. A P235/75R15 is about 29" and are cheaper. A P265/75R15 is about 30.5" tall. Google for p size tires and you can go up farther.
You need to decide what size you want, now much $ you have, and what you are willing to do, along with how much and kind of off road use.
Don't forget, you have been warned about gas mileage.
*And why is it no one ever asks what is the most expensive, hardest way to lift their sammy? (no answer needed)