Should I get a Zebra Finch bird or a rat?

Definitely a rat. Majority of Zebra Finches (besides hand tamed ones) do not like to be handled. They are small birds and easily frightened. They usually enjoy each others company more so than human interaction. They are strictly a "looksy" bird. If you want to be able to hold and play with your pet, a rat would be best. They are also known to be very intelligent, so I would recommend getting a rat.