Most people start off with baby chicks. As
@Obsessed With Silkies said, it's mostly for the experience. Your bond with the chicks will be a lot stronger then starting off with adult hens. Baby chicks will require more time and care to start off with. They need to kept in a brooder (may have to be indoors), and they'll need a heat source for the first 4-6 weeks. If they are being kept indoors you may find them to be noisy, smelly, and you'll have to clean the brooder out more often.
People that start with adult hens normally do so because they can get eggs sooner. Laying hens will start producing eggs about 1week-2 months after you get them (stress from the move makes them stop laying). Other times people get adults because they don't feel like they have the time to raise babies or it makes them nervous. You also know for sure that you are getting hens whereas unless you are getting sex link or sexed chicks, you won't know the genders and may end up with more roosters.
Chicks can be bought at your local feedstore, online hatcheries, or from a breeder near you. You can choose from more a variety when getting baby chicks. Adult hens can be found on FB Market Place, Craigslist, or the BYC
Buy ~ Sell ~ Trade,
State/Country thread. You'll get less of a variety with adult birds. You'd just have to get whatever breeds people are selling if you can not find the specific breed you were looking for. Without knowing where you live or your intended purpose (meat, eggs, dual, pets,) I'd recommend Rhode Island Reds, (Red) Sex Links, Welsummers, Wyandottes, Buckeyes, Sussexs, and Barred Rocks. There are many other great breeds to choose from, so I'd do your research on what breeds will work best for your purposes and area.
I'd wait a year or two before getting a rooster. They are not necessary unless you are breeding.