The best oil analysis lab for DIY Corvetters to use is Blackstone Labs. I have used oil analysis for decades. In that period I've tried several different labs. I like Blackstone the best because they offer the best service for DIYs and they have very good tech support for enthusiasts.
Oil analysis, regardless of which lab you choose, does have limitations. For one thing, it won't take into account contaminants in oil which are so large they are visible, so having your trans oil analyzed is pretty much a waste of time. You should change your transmission lube every 3 years or 36,000 miles. When you change it inspect your magnetic drain plug (if so equipped) and look at the drain oil in the pan. If you see chips coming out with the drain oil, if you see a lot of debris on the drain plug or you see an inordinate amount of fine bronze powder in the drain oil, you likely have a problem with the trans.
Engine oil is a little different. An earlier post says that oil analysis on an engine which has not been sampled before is a waste of money. That's not correct. A lab like Blackstone has analyzed hundreds of thousands of oil samples. Even though a given engine may have no previous oil sampling, through its experience analyzing so many samples, Blackstone can establish a "universal" average of wear metals and if the wear metals of a given engine exceed that, Blackstone's data sheet will warn the user of that potential problem.
Obviously regular sampling of drain oil is better, because it allows the lane to establish a track record for a specific engine, but having and engine sampled which has not been done before is not a waste of money.
For more information on oil analysis visit
Blackstone Labs' web site. Blackstone offers free test kits.