I think there is certainly a case to put forward for reincarnation. I think what has put many people off is the folks that have been on TV etc. stating that they are the reincarnation of higher souls from Atlantis, or Egypt or famous people and so on. If you take for example the 'famous people' bit - there have been so many people who have claimed to be the reincarnation of Mary, Queen of Scots or Cleopatra that if all were true, there would be thousands of Mary's and Cleos all over the planet.
By contrast when you hear the accounts of reincarnation of ordinary lives. People will relate in extraordinary detail about people, places and incidents that occurred long ago. And when the information given is not even known to historians etc. then this is very powerful evidence. There is even fascinating accounts of very young children reciting in detail about past lives - these are some of the most interesting.
As far as my understanding goes - and this is not to say that I'm correct - I don't think you can come back as an animal. You can only reincarnate within your soul group. Since the purpose is to learn and develop. So humans stay as humans, dogs as dogs and so on. This doesn't mean that we can't interact, but that we have to stay true to form. But as I said, this is my understanding and I'm sure others might well have a different view or more knowledge than me.
I know some people will say that they don't believe in reincarnation because they believe in the 'judgement day'. Personally I dont' see why you can't have both. We could get a few spins of the wheel on earth before being called to account for ourselves? But personally I dont' believe in a judgement day as such.