Whatever the manual recommends in terms of SAE grade and API classification is what you should use. For example ".....SAE 15W40 API classifciation CJ-4...."
Remember that as far as API classification they are backward compatible so they can be used in older machinery like something requiring API CH-4 classification oil.
As far as the SAE grade, the base viscosity index oil for a machine is always denoted by the last numbers. In the case of 15W40, "40" is the base oil viscosity that the engine lube system is designed for. That's what you must use if the owner's manual calls for it. It is the "hot oil" viscosity index. The first number, which is the "cold oil" viscosity index, can be chosen for "cold" operating performance. In the summer you can chose 5, 10 or 15. You might also chose 0.
In the winter, to improve starting in cold temperatures, you might limit the cold viscosity index number to 5 or 10, or even zero. There's nothing wrong with using 0, 5, and, 10 designator year around as long as you owner's manual does not prohibit it. However you must use the "40" designator year around.
Thems the basics. Now finding 10W40, et al diesel grade oil is another matter.
I hope this helps you.
(Ref:
540 RAT - Tech Facts, NOT Myths (wordpress.com) )