These sparkly, loud, fascinating chairs, such as the Fisher Price Rainforest Jumparoo, can provide great entertainment for your baby as he or she starts to sit upright, at around six months or so. With a price tag ranging from $50-100, this is definitely not a necessity. Your baby can get just as much entertainment from things around the house.
Pregnant with my third child, a carrier is one of the first things I picked up. You really do need one if you want to have your baby close while doing other things. We use ours instead of an infant carrier when we go in the store, and they are excellent for getting some walking time or other outdoor activities in.
Depending on your sleeping situation, a playard with built-in bassinet can be a lifesaver in the first few months. After that, you are better of baby proofing your home rather than trying to keep an active baby contained in a pen. Trust me, the frustration of trying to keep them locked up is not worth it for you or for baby.
Other items you can easily do without include walkers, bouncers and play mats. If you do get any of these items, try looking at secondhand stores for great deals on gently used gear that you can resell later.