I keep the following:
1. A collection of icecream containers (always useful for transferring eggs to when moving from tank) - also handy for separating larvae into smaller numbers and much easier (first time round especially) for cleaning/feeding when raising larvae.
2. Plenty of water ager/conditioner for waterchanges.
3. Brineshrimp eggs and salt (always a good stopgap if there is no live microfood for larvae)
4. Baking soda for cleaning containers.
5. Spare turkey basters. For feeding or moving hatched larvae and food. I don't mix the main tank ones with larvae ones - and always handy to have spares in case older ones become defunct/damaged (or like my kids used to do = toss them somewhere in the garden).
One of my friends keeps plastic honey jars - so he can post of unwanted eggs to prospective new breeders rather than get rid of them locally or cull them.
Basically that's it.
Foodwise: For newly hatched larvae initially baby brineshrimp eggs, daphnia, ready supply of small baby bloodworm (since finding out where to find them and how to harvest/separate them). During the summer we collect the small mozzie larvae (a mm or so in size), if we have axie larvae to feed, it always goes down a treat, an easy source and mozzie buckets are kept at the bottom of the garden (not too close to the house). As they get larger/older we add the larger mozzie larvae and bloodworm as well as baby earthworms which hatch from the worm eggs in our wormfarms/compost bins.