I have grown both chilli peppers and sweet peppers in pots and they have done really well. They were both potted on from small plants into about 10 inch pots. I have never grown them in the garden as its not really warm enough here. They can also be grown successfully in grow bags - not sure if you can get them in the USA.

if they are going in the ground than about 2-3ft apart. if in pots I grow them in 10" pots too. they are then spaced about 18" apart on the staging.