It really does depend on your other chickens. I keep a grow out pen with juveniles and a couple mellow adults and I tend to put them out at 8 weeks or when fully feathered. Then I monitor them and do a supervised feeding twice a day to make sure they get opportunity to eat and drink without being bullied by other chickens. By the time they are choosing to fly up and roost with the others, they are sufficiently blended with the flock that I need only do normal feeding routines.
I have had adults (a white Cornish, for example) that were too aggressive towards chicks. It is normal for them to run at and peck chicks in dominance displays, but when they persist and chase the chick, repeatedly attacking it, then that is not a suitable bird to be in with chicks. Some roosters are good, some are bad, you really won't know until you try. At this point, I only keep one production chicken for eggs, the rest are my ornamentals and in my grow out pen they are all juveniles of varying ages. My current production chicken is a Jersey Giant and she is very good with chicks. The Cornish went to live with the flock at my mom's, as she was too aggressive to be in with chicks.
I do try to put them out when the weather is decent, around 50 degrees F at minimum. The first few days are the toughest for stress, so I want the weather to be as good as possible for that. About 2-3 weeks after you put them out is when you will see the first signs of disease, if that will be an issue. Once they survive the first month outside, you are pretty much good to go, not counting predators and such.