9/16" is larger than 1/2", the entire screw including the head would simply fall through the hole.
If you are going to use a #8 screw and it's a hardwood drill a 1/8" diameter hole. The depth of the hole should be about 1/8" shorter than the screw length. The point will make its own hole.
If you use a few #10 screws, there you need to drill a 9/64" diameter hole.
If you consider it a softwood, take 1/64" off of the above drill sizes.
Rule of thumb, drill ever so slightly smaller than the screws root diameter.
I would through bolt it using #10 machine screws as they are stronger.