I have real slate and its fine. Not cold but this is a warm house and haven't broken any more things but don't have small children. I think real always looks better. Underfloor heating is great with it
Where are you? I would recommend the firm I used in East London. Definitely get a professional either way. The second time we had it installed by the firm doing our loft conversion I wasn't nearly as happy with the end result (definitely the workmanship at fault though not the product).