Some babies never sleep in a bassinet, cradle, or basket (they go directly to a crib on their first night at home). However, many parents prefer bassinets (kept in their room close to the bed) because they make it easier to keep your baby near in those early weeks when she needs to eat often and wakes up every couple of hours. Some newborns also sleep better in a smaller, cozier space (it's more womblike).
But most babies are ready to make the switch to their own crib by 3 or 4 months. For one thing, they're often too big for their bassinet. Another good time to make the switch is right after your baby drops her middle-of-the-might feeding (just be sure not to attempt both transitions at the exact same time).
To get baby used to her crib, you can start putting her down in there for naps (which will also teach her that cribs are for sleeping, not playing). Many babies love having room to stretch out, and most crib mattresses are far more comfy than thin bassinet ones.
Of course, once your baby can sit up (usually around 6 months), most bassinets, cradles, or baskets will be too shallow to keep her from pitching over the side. For her safety, your baby should definitely be sleeping in a crib before then.