I'm not sure about pot size...but I just repotted my 5 inch barrel cactus and let me tell you, the best advice I can give you is get two more hands! Having a second person to hold the cactus as you fill the pot is a HUGE help.

Here's mine :D I definitely need to repot haha

Yikes. I always heard that 2" wider than the cactus is a good measurement. That is funny! I need to transplant A Ferocactus wislizeni. It is almost at its pot edge but not quite. I guess you bottom water.

For large plants with stiff spines I wrap a piece of carpet or a towel around the cactus and hold the ends of the towel/carpet together to maneuver the plant around without getting poked. It's sort of like having a big, soft pair of pliers.