I quickly found out that the 2wd 1999 Ford E-250 that I recently bought had a open differential. I don't plan to go off-road but I do plan to go off-pavement so I upgraded to a Limited Slip Differential.
This is not a how-to since I had a local shop do it but I thought others might find the info useful. The parts used here apply to my van. The rear axles are by no means universal. This is all new to me so take everything here with a block of salt.

First step was to remove the current differential to get part numbers.
Van de-differentialed:


You're looking at the pinion gear.


Here is a view of the old differential with various numbers visible on the ring gear.
12 07 98 DANA D 47664 P4L578 45 11


It is a Dana 60 unit.
The last two number "45" & "11" represent the number of teeth on the ring gear and the teeth on the pinion.
45 / 11 = 4.090909
That equates to a "4.09" gear ratio

Here is the old unit next to the new unit. Inside the top of the new unit is a set of plates that act like a clutch to transmit torque to both axles if one axle starts to spin too much in relation to the other axle.


A couple close ups of the new unit.


You can just see the words "Trac-Lok" on the top of the new unit. That's a trademark for Dana. This is a OEM unit.

This is how it looked installed.


There were two problems with my install. The first new unit that was shipped had the wrong splines. The van's splines are 35 which is the number of grooves or ridges. The new differential came with 32's. A bigger number means a bigger axle which is more heavy duty. Had to wait for a replacement.


Second problem was the cover. Mine was so rusted the threads came out when they removed the fill plug. Had to order a new one from the local Ford dealer.


Close up:


Final Bill (less tax):
Dana 60 Posi Unit - $445
Carrier Bearings - $60
Bearing Races - $30
Labor 6.5 hrs at $55/hr - $357.50
Valvoline Posi Gear Oil - $20
Rear Cover Assy. - $65
Total - $977.50

Here is a Dana diagram and a parts list. (click pics to enlarge)