Couldn't live without - a sling
Had a baby bjorn to start - was ok but didn't last very long. But we did have another after (I genuinely cannot remember the name, sorry) what was good until 2 years - we certainly used that for close to 2 years.
I used to use it out and about a fair amount rather than always using the pram/stroller. But as a newborn, I used it a huge amount at home!! It didn't help that DD had reflux and needed to be upright a lot, but I would have used it regardless as it meant I could get on with things and DD was with me, and safe, but I had my hands free to do things/carry things etc.
Waste of money - someone got us a nappy disposal unit. Rubbish. Stank. Needed bags. We had a decent-sized bin in the bathroom where we put the disposables, and emptied that daily. (We already had the bin - as we wanted a recycling bin and waste bin combined for upstairs - and it was handy that it was a pedal bin).
I also got a proper bucket with a lid, when I got a number of cloth nappies - to put them once they came off (dry - no napisan or Milton soaking needed), and bring the whole bucket down straight to the washing machine every couple of days. It was handy to then use that bucket for various other things around the house/garden once DD was in pants - until it literally fell apart 2 weeks ago!! (DD is now 14).
1 other thing that was very helpful to have from early on was a Mammas and Papas highchair - it went back to 3 different seating positions, with the 3rd being almost reclined, so DD could use it from early on. And it dropped the legs to different heights, so later was able to be used at the table until she grew long enough for a regular chair. The table tray was removable also, so sometimes she sat in it as a chair, and sometimes it was her table to eat at, play on, paint over.....and as it was plastic, with a removable cover, I wasn't bothered about how dirty it got from whatever source, I could totally dismantle and clean it. It got used in the garden. It spent a lot of time on plastic cloths in the dining end of the kitchen while I got things done in the kitchen and she played with messy stuff. And she could lay back in it and have a snooze while I was working away, when she refused to nap in a bouncer or away from me - but I occasionally needed to not be stuck underneath her and just rocking her (that was nice too sometimes - just not when the 4th washing load of the day needed to be hung out and the kitchen tidied and dinner started and I needed the toilet.....).