What's the proper way or best way to paint a wooden picnic table?

Scorch it with a torch and seal it. Makes a nice look if you like that style.

LINK to wood burned wood

Let it dry if the treated wood is still "green".

Stain with Cabot semi-solid stain (Lowes).

I did a swingset and have been impressed with the longevity.

Kind of cross between a stain and an oil based paint. Will allow some of the grain to show through but it is mostly opaque. Available in quite a few colors.

Hope this helps.