What kind of saw would I use to cut a shape out of a panel?
You'd want a hand held jig saw


Or a stationary band saw


or a scroll saw


You could also do it with a hand held coping saw


But it would be alot of work and difficult to get good square, smooth results with the coping saw.

It takes some practice &amp; skill, and/or a good bit of sanding &amp; filing to get those nice smooth cuts with either tool.  You'll also need a drill &amp; bits to drill out the tighter corners - either of the tools, with the possible exception of the scroll saw, will have some trouble cutting some of those smaller radius inside corners without drilling it out first.