Depends how wide your arena is, we went for 10ft ones as at the time we only had a 20x40 school. A lot of show centres use 10ft, I think Dorset have 16ft ones in their main arena
12' or 10' long by 4" diameter (3.7mtrs or 3.07mtrs long by 10cm diameter) For trotting poles it's very often better to use planks/flat wood so if a horse stands on one it can't role away & possibly cause injury to the horse.
'Standard' BSJA poles are 12' wide, Hickstead and some other large outdoor venues will have 16', and as has already been said, you can get 10' poles too for use at home