I've attached on older CAT D3600 Application and Installation Guide for reference, I prefer to still use the older publication since it only dealt with the 3600 series engine, the newer guides apply to multiple engines and applications.
On page 206 of the attached is a description of the lube oil system, and on page 221 is a diagram of a 3608 lube circuit, 3606 lube circuit is essentially identical, just two fewer cylinders.
Older engines had the factory supplied oil sampling port in the pipe at the oil pump outlet going to the oil coolers, when the G3600 engine (gas engine) came out, the factory moved the sample port to the piping going to the inlet of the priority valve.
Oil sampling for wear metals targets metal particles in a specific size range, if the metal particles are too large, they don't properly process thru the analyzers. So along with oil analysis, regular inspection of the oil filter media and regular maintenance of the oil suction screen is also important.
Here is a link to a resource for excellent info on oil analysis,
There are a lot of links at that page and I think you will find a lot of good info. If you really want to expand your knowledge their book the "Wear Particle Atlas" is an excellent resource, I used it as class material in a class last year and had positive feedback about the material, many engine and equipment manufacturers provided lots of the info in that guide.
The engine oil filters typically don't remove wear metal particles, the standard CAT (and most aftermarket) 3600 oil filters are nominal 20 micron, but your centrifugal filters can remove wear metal particles from the oil stream, so make sure you are looking at the debris coming out of those filters as well, I found the paper liners to be a big help in holding the debris together long enough to get it out on a table and take a close look at it.
Lube oil analysis essentially covers four major areas, wear metals (indications of engine wear), lube oil base stock condition, lube oil additive condition, and contamination. A properly done analysis gives you a lot of info, a poorly done one is worse than worthless because many times it sends you on a wild goose chase. For a good analysis you also need to make sure the lab has a sample of your new oil for proper comparison. If you store oil on site you should also sample your new oil storage as well at regular intervals, usually right after a new oil delivery, that's when all the crap in the storage tank gets churned up and sometimes you may find you're not getting the lube oil you asked for.
So, for your engines preferred sampling method is at regular hourly intervals (250 hrs was the CAT recommended interval), from a "live" location with the oil at normal operating temperature, make sure you also know the total number of hours on the oil, and how much makeup oil you are using if you want best results.
Unfortunately my experiences are much different than TugBoatEng's, I dealt with a number of engine failures and issues due to lube oil related problems, but it was part of my job at the time, and I learned a lot along the way.
Hope that helps, MikeL.