We have family in Clearwater, so wind up taking I-4 from Tampa all the time.
The main problem is if you stay on I-4 all the way to Disney, then you'll have to backtrack to get groceries somewhere, or go further past Disney and then double back. To avoid that we just exit earlier. There are other choices of course, but this works for us. It's a little farther than going to Disney directly, but probably no more than going to Disney then backtracking again to get groceries
From I-4, take hwy 27 north, (I think it will say toward Clermont)
Go about 7 miles to junction Hwy 192.
All the construction on 192 was finished about 1-2 years ago and so now it's really a nice, 4-lane road.
Take 192 east (it only goes that way anyway).
As soon as you get on 192 ( go 1/2 mile, first buildings you come to) there's a Publix on the left. Or you can go about 4 miles further east and there's another Publix on the left again.
After getting groceries, continue east on 192 to the first Disney World exit and head on in.
If you're going to BWV, BCV, or OKW take the Buena Vista Dr exit (That'll be right after the MGM exit).
If you're going to VWL continue in past the entrance gate to Magic Kingdom (be sure you're in the right hand lane as you don't want to wind up going into the park. (or paying a parking fee))
Hope this helps.