I just love trees but what type?

Hey all its me again I Don't have very much space in my garden as you can see from the picture below, its mostly paved and we have two side boxes which we have to keep covered at all times coz of cats I really want some trees. I dont know where on earth I could put them as I want plants along the fence, My sister mentioned maybe I could get some Patio Trees and have them in pots, I was wondering what types you would recommend? Would it be possible to keep them in pots forever and maybe get bigger pots as they get bigger? As you can tell im still learning so advice is appreciated!k-l

 

" I could get some Patio Trees and have them in pots"

Acer palmatum dissectum - either the green or the purple (purpureum) variety ??