My opinion is buy a .22 rifle such as the Marlin 60 or Ruger 10/22 for your first firearm. You'll have a lot of fun shooting those and learn a lot about guns in the process. Plus, they're cheap to shoot.
Start with the rifle; easier to learn to steady your sights when you have a longer barrel and sight radius. You will probably have quicker success with the rifle and less chance of losing interest in shooting.
I still have my first .22 rifle; got it in 1977 for Christmas (did not put out any human eyes, just squirrels').