After the car restraint, there are really only two must haves in my book. A sling (preferably not a baby bjorn style, something like a ring sling, or HAB or Ergo are fantastic) - this makes getting out and about much easier than using a pram, especially in crowded places. It is also great for settling babies with colic or reflux, or any baby really. You can get things done while you soothe them and baby wearing has lots of benefits for baby. Not to mention how useful it is for baby 2. And terry flat nappies - these are fantastic for all sorts of things. In the early days they are the best cloths for spit ups, leaked milk etc. Later on they clean up all sorts of other accidents.

TBH there are very few MUST haves. Some things are nice to haves, but different people find different things work best.

For me, a change table (on wheels with two shelves below) has been invaluable, as I've been able to change nappies at the right height and store all the baby bath/change stuff on it. And in the early days we wheeled it into the bathroom so everything was at arm's reach. But others find they never use a change table.

We found a borrowed bouncer every bit as good as a rocker.