95 Aerostar Transmission (what does it mean)

[Absinthe]

When it is cold outside, and the vehicle hasn't been started all night, if I back out of the driveway, when I shift into drive it behaves like it is in neutral and after a little while (regardless of what I do so far) (perhaps 1 minute though maybe less) of just sitting it will kick into gear.

What does this suggest is wrong? If it is a warm day, or once the thing has been driven that day it doesn't do it again.

[Bear River]

It means the bands are slipping, and do not have enough pressure to engage, most often a sign of low fluid or a leak in the valve body. Time to replace all your fluid and make sure it is at the correct level

[Absinthe]

Does this require flush and such?

Will they know how to do this at Jiffy Lube or do I need to take it to a real mechanic? Or is this something that I could shadetree without much trouble?

[Bear River]

Definitely DO NOT have Jiffylube touch your van. Do this yourself. The flush procedure is posted as as sticky at the top of this forum. This van has all the equipment it needs to flush itself. No machine required. This method does a better job and is safer for the transmission too.

[aerocolorado]

Bear is correct, these transmissions are sensitive to even slightly low fluid levels. Also worth mentioning, per Ford manual: parking on an incline for a prolonged period (overnight) can cause delayed engagement. Low fluid will exaggerate this situation.