What is the intended use of the car? I wouldn't rush to put a cooler on a street car unless you drive like a complete a..hole. Cooler only comes into its own under extreme heat, constant high speed and beating on the car.
In answer to how spec racers are set up- mine is exactly as you described other than I have a non-return valve to stop pumps etc. from draining back overfilling the tranny when not turned on. I bought the required parts on eBay and through Summit and spent about $500 on the whole set up. Kit probably not needed.
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