Let me scan a manual for you first
No need to replace the cooler. Those either leak or don't leak. If its not leaking then its prolly fine. How old is your cooler? The damper prolly is fine too. Mine is the factory damper. No need to replace that unless you just have severe MCOCD.
The pump is the pump.
The kit comes with all plates and clutches. It also includes all gaskets, seals, snap rings.
Here is what I would do. Print out the manual and put it in a binder.
Dissassemble the tranny over the weekend. Mark the pump so that when you install the new pump it will be in the correct position. If you install it 180* off then forward will be reverse and reverse will be forward. This means removal again to loosen 4 bolts, spin a pump 180* and re tighten. Just take a sharpie and mark the pump case to inner bell housing so you know how to reinstall. It's not hard.
Once you get the clutches out and everything apart look at the book and note any broken or worn out pieces.
Order the kit and extra pieces that may need replacing. There is a washer and some brass pieces that I replaced that were not in the kit.
Now after you have this dissembled get on
They have the same kits as everyone else for less money. They have the kit break down of what is included. They also have a piece by piece way of ordering too.
They are online only so not great if you want someone to hold your hand through customer service hence cheaper prices.
Order kit, pump, extra parts if need be (I broke a spring clip during disassembly so wait to order until it is apart, I had 2 orders and shipping due to that clip that was .50 and $5 to ship)
Kit will come fast
Reassemble and go down the road.
I did this on my garage floor. A bench would have been very nice but I didn't have one and it sucked. I left the entire tranny internals in order as I pulled them out (different gears, clutch sections, and casings). Waited for my 2 shipments and put it together.
It is not brain surgery.
If you need to take off a section or piece and label a zip lock Baggie of bolts then do that.
I normally throw everything in a bucket and remember what bolt went where.
The manual will label every piece and show you how to assemble it. If you can read and follow directions then I'm sure you can DIY.