From the Pump i run the oil filter first, main reason is if the motor has a issue it does not fill the oil cooler up with material,
If you get material in the oil cooler, i just throw them away, hard to junk a $500 cooler, i run a Peterson oil screen filter before the cooler to help catch debris.
If you are not worried about debris, then i really dont think it matters what goes first, everything is under pressure, personally i would want hotter oil going into the filter first, it seems that hotter the oil into the filter would increase flow, cooler oil might bypass a % of the oil, unless the filter is large enough to not bypass any oil,
The Chinees filter plates like
@lincster uses is what i use also, i use 8AN seems to be the same as the inside engine gallies,
this is a link to them,
Amazon.com: LineRacing Oil Cooler Adapter fits for Corvette C5 C6 C7 LS1 LS2 LS3 LS6 LS7 / Cadillac CTS-V / LS1 Camaro & Firebird Black (For LS Engine Black) : Automotive
around $30
but the super nice kit have a thermostat in them and will byass the cooler,
Low-Profile Oil Cooler Thermostat for LS Engines (improvedracing.com)
this talks about oil coolers, but you motioned the oil filter
everything listed above is for oil cooler ONLY, you would use the factory oil filter
If you are using a remote filter the best solution is a oil filter adapter replacement that bolt to the filter housing on the pan, unless using sheetmetal aftermarket pan
Canton Racing Products 22-593 Canton Racing 90 Degree Rotating Remote Oil Filter Adapters | Summit Racing
I do not know what pan you have, so they make different threads on different pans for different years,
Low Profile Remote Oil Filter Take-Off Adapter (improvedracing.com)
Some pan filters are Metric some ls oil pans are SAE,