turnston,
I also have a '96 Explorer, here's what I've done.
Kept the stock 15x7 wheels and put 30x9.5 A/T's on it the same day I bought it. Drove those for 2 1/2 years and were very happy with them. Great for everyday use and occasional off roading.
Have since replaced them with 31x10.5 A/T's as my off roading as become more frequent the past year. Still civilized on the street, but better clearance and traction off-road.
Both sizes will fit your stock rims without issue. At stock height the 30x9.5 has no rubbing at all, even at full compression. The 31x10.5 will rub very slightly on the inside of the rear on full compression only. I raised my truck 2" weeks ago, and haven't had a rub yet.
Hope this helps.
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Cheers,
Andrew B.
1996 Ford Explorer 4x4 (slightly modified)
BC, Canada