What do I need to know about having an item of wooden furniture restored?

The two items have arrived safe and sound. As expected, they are solid but show a lot of wear. There’s really nothing to be done for the desk; it wouldn’t be the same if it were fixed up.

But my grandfather’s old rocking chair could certainly regain its former glory if it were refinished and a few tiny repairs were made.

It’s solid wood that I take to be oak. It’s at least 60 years old and probably a good bit more.

I’ve never had anything restored before or had any dealings pertaining to antiques per se.

•  What do I need to know about having it refinished?
•  Is refinishing the same as restoring?
•  Is there a best way to find restorers, or am I just doing a Google search in my area?
•  What kind of questions should I ask, and what would be a red flag?
•  Any idea (ballpark) how much I should expect to pay?

I’m in Northern California.