There are a lot of different options out there for what you can feed them. The normal sequence is Starter for the first 4 to 8 weeks, Grower from then until 20 weeks or they start to lay, then Layer. Some brands of feed offer a combined Starter/Grower that is good until you start the Layer. Some offer a Developer that can be used from 13 weeks until they switch to Layer. Then some people feed Flock Raiser until they switch to Layer. There is no one right answer, just a lot of options that all work.
Do not feed Layer feed until 20 weeks or they start to lay. It has extra calcium for the egg shells. The extra calcium can potentially cause bone deformation or kidney damage in growing chicks. It is not that they are going to fall over dead the instant they eat a bit of extra calcium. It is more of a long term effect if they consistently eat extra calcium. They may never show any effects or they may fall over dead a year later when the damaged kidneys finally give out.
The medicated feed can be a bit controversial. First, you need to know what the "medicated" is in the medicated feed. Usually it is Amprolium, Amprol, or something like that. But it is possible it can be something else. It is also possible it is Amprolium plus something else. Usually it is Amprolium only, but you really need to read the label to be sure.
Assuming it is Amprolium only, some people say there is no problem feeding laying hens medicated feed. Some say they need a 4 week withdrawal period before the eggs are safe to eat. If you go to some government sites, they say that Amprolium in the eggs has not been proven to be a problem, but some also say that it has not been proven to not be a problem. Don't you love trying to translate legalese, especially government legalese? I suspect some of these recommendations might be for when you treat using very high doses instead of the relatively low doses in medicated feed. I am not a medical professional so I don't know who is right. I'm not sure the medical professionals know who is right. I go by what a Bird Veterinarian said. His comment was that it should not be a big problem with the medicated feed since the Amprolium does not move through the intestinal wall that well, but in light of the controversy and differing recommendations, he would recommend a week withdrawal.