The numbers are easy. The higher the number, the thicker the oil. Where you have two numbers, one followed by a W it means the oil has additives in it that make it flow like that number when it is cold, and the other when it is hot. An oil thin enough to flow when it is cold, isn't thick enough to protect your engine when it is hot.
The longer lives of today's engines may be largely due to the multi grade oils common now. By the time I had a car of my own to care for, I always used the multi grade oils, usually 10W-30, and now 5W-30.
I will leave the synthetics to others.