I've had 22's, 20's and currently 18's. I have felt no difference in the ride or gas mileage with 18 vs 20. In your case if you have the money and plan to do very little off roading go with the 20's. As far as 22's stay away IMO!

 

I've had 18's and now 20's and there is no difference in the mileage unless you go up in tire size.
The wheels themselves will not affect performance. When I was running 18's I had 38.5 pro comp AT's and my mileage did suffer a little like 3-5 mpg from the 35's I starterd with when I first lifted mine. Now I'm back down to a 36" but on 20x14 Fuels and now I'm just about back to where I used to be before the 38's on mileage.

On 38x18 Boyd Cottington's here:





Now on 20x14 Fuels with 36x15.50 mickey's:

 

With pricing aside, a 4wd '04+ F150 is so fitting with a 20" wheel it looks like a standard match.

Here are my 20" wheels on 33x12.5 Toyo M/Ts with a 100% stock un-leveled suspension.