My little boy has just turned 12 weeks and our baby swing has been invaluable! We have the Fisher Price Rainforest one which we nabbed 2nd hand from eBay, he loves it. Other must-haves have been Little Grippers socks (they have a band of that rubbery stuff like on hold-up tights and stay on brilliantly!), my Skip Hop Stroller organiser, and the cup holder that I finally (and reluctantly) spent a tenner on!
We love the MAM bottles and microwave steriliser... used them with my daughter 5 years ago and have stuck with them this time around, also the MAM brand dummies.
Lidl/Aldi nappies are both brilliant, I won't use any wipes other than Huggies Pure (nice and thick with good wetness and no "soapy" feeling!), and a generous layer of metanium ointment at the first sign of soreness stops nappy rashes before they develop.
Trying to think of any other invaluables but my brain is failing! We've made some big boo-boos too... thought that we didn't need a "decent" travel system 2nd time around because he'd just go in my daughter's old MacLaren when he reached 6 months. It turns out that 6 months is a bloomin' long time to be faffing about with a rubbish pram and non-isofix/easybase car seat. We've had to buy twice because of that mistake.
Wish I'd known about that Tommee Tippee bottle prep system a couple of months ago! Am going to download a white noise app now... keep the recommendations coming!