Ammo selection for an old 550-1

Hello all. I recently pulled out this old Remington that my father gave to me right before I moved across country. I love this rifle, it runs great and hardly ever malfunctions. The only malfunctions I have encountered are when casings don't fully eject before the receiver tries to close. And I attribute that to using the old ammo that came with the gun.

I would like to use this rifle for squirrel and rabbit hunting. Ive seen people have trouble and cause damage to their old rifles by using over powered ammo and I want to know if there is a clear choice for what I want to achieve with this rifle. Thank you for any advice.