Oil/Fluid and Battery Questions

[FNG90-195]

My car is still at the shop where I initially saw it. It was a customer's car in for repairs over the winter (starter motor). I haven't brought the car home yet. Before I do, I would like to have the shop change the fluids, as there are no service records with it, or even a glove box manual to tell me what to use.

From reading a number of threads, I have determined that I will be using the Amsoil AMO 10W40, Bosch filter, and green antifreeze with glycol that meets GM 1825specs. (did I get all that right?)

Now for my question: what to use in the transmission and differential? what weight, and is it synthetic?

Also, I just thought - is there any kind of a filter or screen in the transmission?

I know I need to replace the battery as well, and I will use an AC Delco. Can you tell me the group and model # of the correct battery?

Anything special I should tell my mechanic before he proceeds? He has a C4 himself, and is pretty knowledgable, but I'm concerned there may be some special things to do or worry about. I've never had a car as advanced as this. I usually worry about replacing rotor and condensor and setting points!

Any advice would be greatly appreciated.

Thanks

Mark