What is the difference between the Waterii and Anagyroides?

On the poison question the seeds of all laburnums are poisonous. Just tell your children not to eat them, the animals wont in any case.

I'd recommend you buy Laburnum watereri "'vossii' - this particular variety produces very little seed, and also has the longest racemes (flower heads) of all the varieties. Anagyroides gets a little taller and produces much more seed and has shorter flowers. The point about the seeds being, of course, that they are highly poisonous, so the fewer you get, the better.
Forgot the rest of your question - plant October/November, water well if you do it October. Being in a corner will be fine, but remember to leave about six feet behind the tree to allow it space to develop a crown as it grows - eventually, the crown will be up to 20/25 feet wide, and hopefully higher up than any fences or walls in the corner.