What tye of oil for 84 Olds with 307?

I would throw some ZDDP additive into it since it's running flat tappets. There are also oils designed for flat tappet engines but they're generally more expensive and have to be special-ordered.

Downside of the ZDDP is it can poison a catalytic converter (combine this with manufacturers switching to roller lifters and that's why it's significantly lower now), but it can only help the engine unless you overdose it.

You should be fine. Any good brand name, Pennzoil, Valvoline, etc. would work. Mobil is okay also.

And 10 W 30 is pretty much used by many cars.

Todays oils are far better in every way than anything produced 30 years ago. Kick whoever it was that told you otherwise right in the nards.

10W30 is good for most climates and older engines. They were baffle you with bs. Don't use a synthetic.