Don't over think the brand of oil, oil brands are like religion; use whichever brand you worship. Said another way, regardless of which brand you use, assuming you use the correct grade and keep up with your oil changes, the engine will outlast the rest of the car.

As for grades, I use 0W-20 in both of my high mileage Honda engines, that oil is superior in every respect to 5W-20. Regarding 5W-30 (or better yet, 0W-30), yes, with 200,000 miles on the clock, you certainly won't hurt your engine by going with the heavier oil, you may lose a little fuel economy, but that's about it.

 

OP's car is a 2002. The following is from the 2002 owner's manual:

 

If the car has had synthetic in it so far keep using synthetic, specially at this mileage. As far as viscosity goes (you haven't provided enough information like if it leaks or burns, etc) and everyone and their grandma will have differing opinions. However, All things being equal, I would run 5w-30 regular or synthetic based on my first point. Wether you choose a high mileage blend will depend on other factors (agan you have not provided enough information to make the BEST suggestion) but most of the time I would NOT recommend a high mileage blend unless the engine has been using it for a long time.

 

What do you believe the benefit would be of using 5W-30 versus using the factory recommended 5W-20 grade?

 

Simply because a higher mileage engine has higher internal clearances (out of spec, worn out). A 5w-30 oil will help with this all things being equal. It might increase the pressure slightly also which is not a bad thing at 200k miles. This is why people have traditionally added thicker oils to engines that burn thinner oils as a band aid. There is nothing wrong with doing this. You are proportionally adding the type of lubrication the engine needs as it ages.

 

For a worn engine I agree, 5W-30 may be a good idea; that said, just because an engine has 200,000+ miles on it in no way means the engine is worn to that point. The J30 in my 2001 Accord is a good example of this, it has over 200,000 miles of use, was lubricated with nothing but 5W-20 for the first 114,000 miles (per the first owner's records), and nothing but 0W-20 since I purchased it in 2012. It still doesn't use even a half quart of oil in a 7,500 mile oil change interval, and the oil pressure has never been an issue. For Honda engines of this generation (regardless of whether they are the I4 or the V6 variety), unless they've been abused (either in how they were maintained or how they were driven), there is zero reason to think there would be any benefit from a switch to a higher viscosity oil.