Hi, welcome to the UK and to our sunny part of south London!

The list of places to go is endless so don't really know where to start apart from saying yes to all your questions! I've lived here for a long time and have never contemplated living anywhere else in London as its simply such a nice area.
Its fantastic for young children, there are lots to do and loads of parks, play areas, great schools, etc. I've never experienced any crime but I do know people who have. Muggings are still fairly rare but they do happen as to break ins and car thefts. Having said all I still feel relatively safe in this part of London. I think you'll be fine here.

Have a look at the various threads on this forum as you will probably find the answers within.

good luck