Graco infant seat, or Britax car seat, Maclaren strollers-good to 55 lbs (we have a Quest), Angel Care baby monitor (has a sensor that sounds an alarm when baby stops breathing), Pampers diapers/wipes, lots of pacifiers (if using them) with retainers (I like Mam, and Nuby), when they get older, there are pacifiers that close when dropped (you will be opening them all the time if theyre too young to do it themselves), convertible crib and furniture that can be used through their lives, portable swing (ie Fisher Price), Halo sleepsack, pack and play with extra sheets (I like the quilted ones), Leap Frog toys (love them), Baby Einstein crib thingy thats a turtle-lights up, fish swim around and it plays music (dd loved it and still does at 2 yrs), boppy for nursing, Avent products (pump and bottles), Hotsling or something similar (I hated my Bjorn-hurt my back. My babies prefered the Hotsling), Desitin (though I switched often when one wouldnt work), Baby Eistein under sea playmat, doorway jumper, one of those cheap battery powered push on/off lights for night time diaper changes as they dont put out a lot of light, but enough to get the job done. A friends son who is 5 also has one next to his bed which he turns on when scared at night, a nightlight, rectal thermo (the others arent accurate for infants, but are handy to have as a tester before having to put your baby through the agony!), vaseline, Aveeno for babies (lotion), Johnson & Johnson stuff, bathtub for the sink (love the one I had-blue with a sling support in it), toys/mirror for the car (dd liked Fisher Prices aquarium mirror with a remote for me. It lights up and plays music), a mirror that attaches to your rearview mirror so you can see your child, sunshade for the car window, JJ Cole car seat/stroller bunting (living in SC the lightweight version was fine for us-beat having to layer your baby with clothing), gate for stairs when they start moving, bumpers for around furniture (I also used stick on foam pipe insulators or furniture edges, and cut up a swim noodle to stick over drawer knobs, cabinet locks are a must too (I like the magnetic ones as the kids can eventually open the push tab ones), furniture tie downs, fire alarm in bedrooms (they make one now where you can record yourself telling them to get out which has been shown to wake the kids more often than the standard ones), and lots more safety stuff (its amazing of what all is available these days compared to when I was little)!
Skip the wipe warmer- they dry out the wipes and can be a fire hazzard. Also the Swaddle me (a blanket works just as well if not better. My dd actually got tangled up in her Swaddle me and it was over her head. Luckily I was a light sleeper and heard her crying!