Just inherited 1999 C280 with 38,000 miles on it. Should I take it to a dealer and have diagnostics run before using it on a daily basis?

Yes, have it checked out first. A Mercedes properly cared for can last forever, BUT, as most mechanics will tell you, Sitting for long periods of time with little use just kills them. You NEED to drive it regularly - even if for only a short while. 10 miles at a time is not enough. There are a host of service items that are probably needed because of its age - not its miles. Get those done and you should be fine - do have your mechanic check for dry/cracked seals. This would be from not being used. If there is no leaking of air or fluids - then you are good to go. Some items that need to be done are brake fluid flush and transmission filter and fluid. These are important - but do not have to be done by Mercedes (unless you just like paying to much).