I just had my third child, and my second 2 are only 17 1/2 months apart. (I have an 11-year-old, a 21 month old, and a 3 month old) This was my basic list:
*Double stroller - I like graco.
*Clothing - even though I had all the baby stuff from the last one, the seasons were opposite so I found that my October baby couldn't share much with my late April baby.
*Second crib, dresser & changing table for new baby's room. This way I was able to do midnight feedings and changing without waking my toddler by going to use the changing table in his room. Check CraigsList, you can find nice stuff for good prices there.
*Pack & Play for the living room - my toddler likes to try to pick up baby, so the floor is now out of the question even for the baby gym, I put that IN the pack & play and used it there to protect the baby.
*baby bjeorn - I put the toddler in the grocery cart and carry the baby that way, not just at the grocery store, I use that thing a lot.
*bigger diaper bag - who wants to carry 2? make space for 2 babie's stuff in one bag.
*baby monitor for 2 rooms - sold at babys r us. I tried 2 different monitors but they interfered with eachother and I could never tell which child I was hearing.
Make sure that every baby seat/swing has seat belts that WORK and can adjust to fit your newborn, I found out the hard way when my toddler actually took the baby out of the bouncy seat and dropped him on the floor! (he was fine, just scared)
Sounds like we have a lot in common! Keep in touch and good luck!