What kind of motor does it have?

If it is a Briggs engine, there will probably be an owners manual and other data available on their site. All you will need for them is an engine number and model which is usually on a metal tag.

30W, 10W30, or syn. basically as long as you put oil in it and keep if in the XXXXXs. more better would be the eye candy when you change it and see the nice clean oil on the dip stick knowing if it fails it wasn't cause you didn't change or check the oil!!!!!!!!!!!!!

More important then the type of oil is to see to it that you change it about every ten hours of run time.

I have an 8 HP B/S from the same vintage. My manual states for the 5 HP Tecumseh - Summer - SAE 30 (substitute SAE 10W-30) Winter - SAE 5W-20 or SAE 5W-30. Use Service Classification SF or SE. Of course I think we are up to what SM now. Capacity states 19 oz for the 5 hp.

Same basic recommendations for the 8 Hp. I run straight 30W and as others have stated, change often.