Engine Oil Cooler Install

Thanks for all the replies and comments! A lot of great information to go through. Couple more questions, cause I seem to have the ear of some experience people here.

I'm definitely going to avoid the transmission cooler, I was worried about restricting flow, but thought I'd ask cause I had it sitting around.

Another option I have is this cooler: Setrab SLM Series Oil Cooler, 14 Row, M22 Ports, 420mm Core - Pegasus Auto Racing Supplies
My father in law had an oil cooler kit to install on his BMW (I know...I know) but it wasn't going to work on his setup for some reason, so he gave me this cooler if I could use it. Does anyone have any idea/opinion on if it would provide enough flow for my application? Length from tank to tank is 19", height of core is just below 5", thickness is roughly 1-1/4".

Planned on running it with Canton's universal sandwich plate, which is roughly the same as their relocation plate, except I can retain my stock oil filter location. It's got 1/2" inlet and outlet ports, and the oil coolers inlet and outlet port are about the same. Planned on running -10AN fittings and associated lines.

Also, the 360 this is going on isn't that high HP, only about 400hp with about 420lb/ft torque. Nothing too serious, but it's going in a daily driven (during the summer) Lil Red Express. I'm adding the cooler for more of a piece of mind (cause of the filled block) more than anything.

Thanks again!