I think that 10'x6' is too small for 6 chickens. Will appear great when then are small, but they grow fast. Better to have fewer than too many for the space. The idea of bantams might work well for you but if you go for the larger breeds, I recommend 4 for that area. Overcrowding will lead to heartache for you and fighting, boredom, unhealthy conditions for the chickens.
I do not think it is cruel to have chickens if they cannot free range, but I think you have to pay attention to some basics that really apply to all of us.
Predator proof is vital.
Keep the run clean and give them branches or areas where they can get off the ground during wet or muddy periods. Water changed often, nutritious chicken food and treats
Do not keep a rooster in this small space...you don't need one
Give them treats, set up a dust bath area, give them something to scratch around in ( I use straw in my run which is easy to clean out and will soak up some rain during the winter months.
Let them out with you as often as you can or you go in and sit with them
Teach them early on to come to you using treats so that when you do let them out, they will come back when YOU want them to.
I allow mine to free range when I am home but there can be several days in a row when they don't get out at all. They seem happiest during this time when they are clean and dry, fresh water and food and exercise...even if it is hopping up and down from the branches in the run.