Best joint for pine storm windows? Mostly why not miters

In my experience (midwest winters), storm windows are generally more for extra insulation purposes than severe storm protection.

You can install exterior or interior storm windows, and they can be of varying degrees of sturdiness. For places that do have more extreme winds, you can buy windows that are engineered to absorb a hit from flying debris. I'm not clear on why you would wait until winter to install them in that case (post-hurricane season).

You remove the screens if there's a concern that wind can rip them out or snow drifts can tear the screen from the frame. As @Steve Armstrong points out, you could also remove them for cosmetic reasons since they're serving no purpose with the windows closed for the winter.

In your case (and my current home in Houston), I wouldn't think either would be a necessary winterizing task.

First measure across the window, door, vent from the inside of the exterior trim to the outside of the exterior trim on the other side. Do this vertically and horizontally. Then add 6-8 inches to BOTH measurements, this is the size of plywood you need. You add length and width because you don't want the plywood pushing on the glass.

The thickness of the plywood is a personal choice, I would use 3/8 or 1/2 inch, but remember 1/2 is more expensive and weights more. I have never had problems with 3/8.

When you attach it to your wall, you can do things quickly or carefully. This depends upon what the exterior of your house is, how much time you have, and how often you see yourself doing this in the future. You could just screw the plywood to the wall with a long screw every 12-14 inches. OR you drill holes into the boards, hold it to the wall, mark the hole locations, then drill into your house and use a tap and die to make a more permanent screw hole.

The former option is preferred if you don't see yourself protecting your home that often. But if you live in tornado alley, I would definitely upgrade to 1/2 inch and use a tap and die for strength and convenience.