These are just some of the products I really like that specifically relate to preemies, though I think some would work for any new parent. I've only listed out the things that I personally use and highly recommend. Feel free to email me if you have any questions about anything I've listed here!
Fisher Price Rock N Play Sleeper - hands down the best nighttime sleeper for babies with reflux or need to sleep on an incline. I find that I need to use the belt at night to hold the baby more upright because she tends to slide down more as she gets bigger. It's really lightweight so I can move it from room to room easily and it sits up high enough that I can easily reach it from the bed.
Itzbeen Baby Care Timer - This lets you set the time intervals for feeding, medicine, diaper changes and other stuff. You just hit the button when you've fed the baby and it starts the timer over and will either blink or sound an alarm when it's time again. This is GREAT for me for remembering when to give Scarlette her medications. Also, it has a left/right switch for remembering which side you breastfed on last, which is really great if you're like me. When we were breastfeeding, I tried the whole hairband-on-the-wrist thing and then at some point I'd pull my hair up in a ponytail and when it was time to feed the baby I'd be all "Wait, where is my hairband?" This is definitely in my top 3 baby products list.
Dr. Brown's Bottles & Preemie Nipples - they are made in a way that reduces air so it helps with reflux. Also, they are BPA free, which I just prefer.
Boon Inc. Grass Countertop Drying Rack - okay this may seem crazy but it is the absolute BEST for drying pump parts. Seriously, washing and drying those suckers was the most dreaded part of my day until I received this as a shower gift. Worked so much better/faster than just laying everything out on a towel or hand drying.
Halo Preemie Sleepsack - most preemies really like to be swaddled but honestly I don't use it for sleeping - I use it to swaddle Scarlette really tightly to put her feeding tube down. It works excellent for that but b/c of that, I once tried to put her in it to sleep and she screamed like a banshee. Apparently it had bad associations for her. The swaddle part is removable though, so I am able to use just the sleepsack, I just pull her monitor wires through the armhole and tape them to the bottom so they don't come up near her neck at night.
Chicco Cortina KeyFit 30 Travel System - ours is in Bella. Our NICU gave us specific measurements the car seat had to have. After lots of research, this had great safety ratings and the biggest thing we looked for was a car seat that would not let her head tip because in micro-preemies, any slight airway obstruction can cause an apnea episode. You so do not want that taking place in the car. It is a bit heavier to carry than other car seats. Also, it does NOT have grooves to sit in a shopping cart- this was purposely done as a safety feature as placing carseats in the front shopping carts is a saftey hazard. I personally really like that about it.
Little Twig Unscented Extra Mild Body Wash & Lotion - this is unscented but it smells so good! It is one of the only sets that didn't give Scarlette a rash- we tried a lot. This one is really mild, hypoallergenic and paraben free. And also? She didn't cry that time I accidentally got it in her eyes. I cried because I felt like a terrible mom but she was all "whatevs, yo"
Salter Baby Scale - This is the scale we have, I have to weight Scarlette every day and chart her weight for her drs. She has to gain 1/2 to 1 ounce each day to stay off the feeding tube. This isn't quite as accurate as the hospital scale but it is very close. I like that I can set it to weigh just the diaper and then it calculates the diaper weight and subtracts that from each baby weigh-in. That way I don't have to weigh her totally nekkid because that results in her peeing all over the scale. I also like that I can switch to the metric system b/c the doctors are always asking me for that number and I can't convert in my head. And it transitions to a toddler scale for when she gets too big to lay down.
Vaseline Healthy Hand And Nails - the skin on my hands was peeling off from scrubbing so often. This is the only lotion that helped. I still sleep with it in gloves and I don't know that my hands will ever fully recover. I don't know how the nurses do it!
(Note: some products contain affiliate links, you can read my disclosure page here but basically that means if you buy something through the link, it gives me a little percentage which helps pay for this webspace. I've only linked to products that I use and highly recommend)