Gosh. Good questions.
Modern striker-fired Composite handguns are hard to beat. I'm sure you've heard of Glock, but Canik has a much better trigger mechanism than the glock, which means more accurate shooting (and they're cheaper). Smith&Wesson, Springfield are a couple other makes that have similar offerings.
9mm is a good starter caliber. Light recoil.
I have lots of fun shooting 22s of any kind. I have a couple pistols - Ruger Mark V is fun - and a couple of rifles - a cheap one is the Winchester Wildcat 22. 22 ammo is the cheapest there is. You can shoot all day for $20. Not so with almost anything else.
Most important thing is safety. Take a firearms safety course. After that, take a shooting course at a local gun range. Will be worth it to help with shooting fundamentals and learning the right way.