Chicco Keyfit 30 Car Seat. This was the most recommended car seat we found, so we got it. Super easy to install and to get out of the car. My only complaint about it is that it is on the heavy side, so when you add the weight of a baby in, it can get extra heavy very quickly. That said, we've loved it and I'd buy it again (and I had a heavy baby!).
Uppababy Vista. Let me level with you: this is an insanely expensive stroller. HOWEVER - it accommodates up to three kids, so it's the only stroller you'll ever need to buy. Several people told us that when they had their first child, they bought a one-child stroller, and wish they'd gone ahead and sprung for one that accommodated at least two children because they eventually had to sell the one-child stroller for much less than they paid, then buy a second stroller. The Vista is extremely durable, gorgeous, and handles like a dream. The stroller base stands up on its own (almost like a kickstand) so you never have to worry about propping it up on anything. Extremely easy to assemble/break down, and comes with both a bassinet and a rumble seat, so it grows with your baby. In fact, I know several people who've used the bassinet of this stroller as the bassinet in their bedrooms - double duty! We asked the women in our families (aunts, sisters, grandmothers, cousins) to put money toward this stroller instead of buying a baby gift, and they generously funded a large portion of it.
This is not a jogging stroller, so if you're interested in one you can run with, there are lots of great, lightweight ones on the market. The Bob is one that I've heard really good things about from several friends.
Momaroo. People either swear by this product or don't use it much. I was very glad I had this for the times I needed it, but Mac spent more time in the Rock-n-Play or in his crib. If you aren't sleep training right away, the Momaroo is wonderful for little naps and having a place to put the baby so your hands can be free during the day. It was 6 different swing motions, a built-in sound machine, and is Bluetooth enabled so that you can play music through it. My only "con" about the Momaroo is that it is heavy and cumbersome to move to room to room, so I wouldn't buy it if it's going to be your only swing. If you have a Rock-n-Play or another lightweight rocker/swing (like a Baby Bjorn bouncer, for example), you'll be set!
Graco Pack 'n' Play. I love this product, but I've also heard people swear by the Baby Bjorn Travel Crib (which is more expensive, but much lighter-weight). You need something to take with you when traveling.
Boba wraps. Love these things so much. Easy to use (once you get the hang of it) and easy to roll up and stuff in a suitcase or diaper bag. People also love baby slings.
A 360* carrier. This is another must. At a certain age, many babies stop tolerating facing inward in carriers and want to face out so that they can look around! If you get a carrier, make sure that it's capable of front-facing when the baby is younger, then facing out when it's older. Any brand will do the trick - we have an Infantino.
Diaper bag backpack. This style of diaper bag is great because you're not carrying it in addition to a baby. Find one that stands up on its own (maybe even has feet on the bottom) - great for doctor's appointments when you can't fool with using both hands to go digging through the bag. We have this one and love it.
Nest Cam. We use this as our baby monitor and I truly don't know why people use anything else. Nest Cam is the same price as other monitors, but doubles as a beautiful, sleek, and aesthetic home security system. It's accessible from ANYWHERE - it never goes out of range because it's connected through your WiFi - so you can access it from dinner or a movie if you go out and leave your baby with a sitter (not that I've done that...hehe!). It has night vision and the a microphone feature so that you can talk through it if necessary. It's so lightweight that we always travel with it and it's a cinch to set up anywhere we go. A Top 5 product for us. I recommend it to everyone.
Feeding.