First thing that comes to mind: Are you going to change gears with the substantial increase in tire diameter? What ratio does your rig have now? Be aware that with 32's or 33's, and stock gears, performance will suffer. Your mileage will go down also. I run 33's with 4.56 gears and get about 15-16mpg around town, maybe 17-18 on the highway. It gets better mileage with 4.56 gears than it did with 4.10, since 4.56 matches the stock engine rpm best with 33" tires.
As far as ride quality, it's all a matter of personal preference. A bigger tire is likely to be a little more bouncy than stock, although you can control this somewhat through air pressure management. Remember, since you're increasing the volume of air in the tire and the vehicle's sprung weight is roughly the same, you can run a lower pressure, which will help your ride quality.
Are you going with an A/T tire, an M/T? The more aggressive the tread, the louder it will be. Also, since you're keeping the same wheel diameter but increasing the sidewall height, it's going to lean more in cornering. As far as "shimmying", a wider tire will be more apt to follow ruts in the road that a skinnier one. Bigger tires and wheels also weigh more too, which will decrease overall performance. After saying all this, none of it is objectionable though. It is a little different, but you'll get used to it.
Are you sure you can fit 33's with the lift you have in mind? I'm not up to date on lifts for the newer Explorers, although I'm sure others on this site are.
Whatever you choose, I recommend doing as much research as possible before making a decision and spending that hard earned cash. You'll save money in the long run.
Good luck and keep asking questions.
