Having run the 4R70W and 4.88s. Sort of wrote the book (the 20+ year old tech article before the full Explorer swap was real).
I will say 5.38s. Here is why...
Street use, you are not running it hard enough for the small tooth to be an issue.
The stock 5.0 Explorer you said you are planning on running doesn't make enough power to hurt the small pinion. There are people putting exponential levels more power through 5.38s and not hurting them. Small pinion is not an issue for you.
37" tires are tall, lots of drag, rolling and wind. You need to help that little 302 to stay in the happy spot while pushing all that drag.
A 5.38 gear will get you 2000 RPM at 60 MPH, 2500 at 75, and if you try and run 90 it is only turning 3000 RPM. Really isn't that deep of a gear. I question of there is enough torque at 3000 to actually push that rig at 90, but you really shouldn't be doing that anyway. 75 is fairly realistic, and 2500 RPM puts the 302 in the power band where it might actually be able to push that wind without being on the floor.