The first thing that I found to be a must have for a baby is a bouncy chair. This is probably my most used baby item. It provides a place for the baby to rest when they are little without taking a lot of room and gives the baby a place to sit up and watch things as they get older. Additionally, most bouncy chairs now come with additional options and toys, such as vibrating, playing music, or having a toy bar. These features are often a great thing to use to distract the baby for enough time to allow mommy to get things done.
Another item that I cannot live without for my children is a small chair that allows them to sit up before they can sit up on their own. For my first two children this was the Bumbo and for my last baby, a chair just like it. The only concern with this chair is making sure that the baby can hold his head up by himself. With this chair, the baby can see what is going on around him and he is often happier than he would be in any other chair. This chair can also serve as an alternative to a high chair. I tend to feed my baby food on the floor during the first few months of eating and this chair puts them at the perfect height.