6/'87 325is approx. 200k miles

I am interested to try 15w40 or 10w50 non-synthetic oil, Bentley manual says ok to use just like all oils, for certain temp. ranges, but I am not familiar with what product factors to consider. There are HD (heavy duty) labeled versions, labels for diesel engines, etc.. Should I be concerned about these labels, is there a particular designation I should choose? Where can I get something good for inexpensive?

I searched the forum and saw a couple suggestions of non-synthetic 15w40 Shell Rotella oil. I also saw a reference to Castrol Rx Super 15w40. I didn't see in my search of these products that they mention they are specifically non-synthetic, how do I know?

I don't want to get into a debate on what oil to use, I have just found it hard to time my oil changes, since I don't drive my car that much, to what Bentley manuals says to not use 10w40, above 50 degrees. I have had some hard starts and car feels sluggish at times with 20w50 when temps. in 20-30 deg. range. Looking for something with a better fit to use in that 'sweet spot' of temperature ranges.