Pistol or Rifle?
Go with a .22 cal. Ammo is inexpensive and you can shoot all day for less than $50 as a brick of 500 will run you as low as $18.
I like my S&W Victory, was looking for a Ruger mark 4. But for the price I couldn't pass it up. However for a beginner, any .22 cal pistols in the $200 price range will still give you good accuracy without breaking the bank.
One thing you could do is many ranges do rentals. Doing that will allow you to shoot multiple guns without the worry about having to clean them.