New CPO E53, Should I baseline it?

[Best4x4xFAR]

Hello All,

We finally settled on an '06 3.0 E53 that was offered as a CPO at a local dealership. It is pretty much everything my wife wanted, except its not a 6-speed manual (like finding a needle in a haystack, she gave up). I have the service history, and it has had pads and rotors replaced, but looks like it has only had one oil change (??) in its 45K life. I hope that just means it wasn't done at the dealership all the time.

Dealership is not able to give me a straight answer on the last time fluids were changed, so I was thinking it might be a good Idea to baseline it (change out all fluids, and start new maitnenancelog). It is still under the Factory serice plan as well, but this only covers scheduled maintenance, so I am sure this is on me to fund.

Any thoughts on how far I should go, recommended fluids, etc? I've always been a fan and user of RedLine Oils, so I was thinking I'd go Redline for the engine and differentials, but not sure about the auto tranny (our first). I'm assuming its best to get a replaceble oil filter element from BMW, or is there a better alternative? Looks like folks also recommend BMW coolant specifically?

Thanks in advance. I'm searching and reading enough threads that my eyes are going blurry, so I apologize if I missed a well covered topic.