Having had a flight with a friend in his AA5 I have had to add that to the list of aircraft I cannot fly safely. I learned in a Cessna 152 and have done my conversion to a DA40TDi. For myself, this was the right way to do it as I find the DA40 very similar to the 152 to fly in that it is very responsive but the 152 is more versatile and forgiving. I still find it odd that I need to use flaps for a normal take off in the DA40 and find the requirement for full flap for landing much more restrictive than the 152. My preference would be to do it as I have done - 152 first (yes I know they are old and probably look a bit scruffy but so what?) but you have to fly them and, I as find, unlike the PA28 and Tomahawks they they are much more responsive and far less heavy on the controls. You can then do your conversion to the DA40 in a shorter period and probably save money which is always a bonus. I am only 1m55cms tall (or short).
Do your training in the UK, it may take a bit longer but you will learn how to cope with a lot of controlled airspace - they don't seem to have much of that(from what I have been told) in the USA. I have also met several PPLs who have come back here to do their ATPLs and convert their FAA licence to a UK one. They have all found difficulties in coping with the differences and have needed up to about 20 hours further training to get themselves up to a satisfactory standard. Not much cost saving there.
If you then need to do some hour building I would suggest going to West Australia which has an excellent climate, the busiest GA airfield in Australia and a very good exchange rate.