The hole for the dish should be BELL shaped, smaller at the top than the bottom. 20" at top should be enough, but the top should harden raised dome shaped to keep water from sitting there, you want that to drain off. I've done plenty of these, and that's the best way to do it.
At the bottom which should be tamped down, you put a bag or two of river gravel, level it off, then place a flat cement patio paver in the middle. Then, you put the bottom of the pole on top of the paver. That paver keeps it from sinking into the ground before the cement sets up. The gravel helps drain and keep ground water from lifting the pole. Then, you use long 2 x 4's strapped to the pole (and staked to the ground) to keep it up and level as you pour in the cement. The 2 x 4's get removed after a couple days/1 week when you feel your cement has hardened. With a hole the size you are talking about, you are going to need about 1200-1300lbs of cement, perhaps a bit more. Cement is cheap, do it once, and do it right the first time!
Don't forget that before you put the pole in the ground, you should drill a hole through it and place a long bolt/all thread in it sticking out from each side some inches. That gets embedded into the cement, and keeps the pole from finding a way to eventually spin (due to wind load, or whatever)
Make sure you use a good level, and it should be leveled North-South, AND East-West. Make sure it's right BEFORE pouring the cement, and check it several times while pouring the cement. Once all the cement is poured, you aren't going to easily be able to change it if it's wrong. You also pour that cement evenly all around the pole, not just in on one side.
As for wiring, you can go to Lowes or Home Depot and buy some coiled black drainage pipe to run in a trench from house to dish, and have it put so the cement will harden around it, and later strap it to the pole, (don't have it strapped while doing the cement work). That protects from wives with a gardening shovels. Use a large diameter size, so you can pre-pull all the wiring through it, and you might also pull a small/thin nylon rope through with the wires (comes in handy if ever have to pull additional wires). PULL SPARE EXTRA WIRES right away!! Trust me on that, you need extra wires for later, in case some goes bad, or even at least a couple coaxes for easy future changes/additions.