Personally, I am mainly interested in beers and wines. For jams, chutneys, cakes, etc., you probably have all the equipment you need in your kitchen. A preserving pan is useful if you are making large quantities of jams or marmalades but not essential.
As far as brewing is concerned a thermometer is a must, as is a hydrometer. Brewing buckets, demijohns and bottles should also be on your list. Wine can be siphoned from a demijohn as and when needed but beer needs to be bottled. You need undamaged bottles and quality crown corks along with a decent tool to do the corking. In the early days I had a shaped lump of metal with a short handle that that you had to hit with a hammer! After a few accidents I drilled a hole in it and concocted a lever device out of conduit that served me well for many years.
Corks for wine bottles seem to have deteriorated over the years and these new plasticy ones are not to my liking.
I now prefer to use Novatwist plastic screw caps for my wine. They are a lot more expensive than corks but so easy to use – they look good too!
As far as sterilisation is concerned, I use VWP for cleaning bottles, demijohns and buckets. Towards the back of the picture above is a container of Star San, a high foaming, acid anionic, no-rinse sanitiser. You only need a drop of this stuff to sterilise a battleship! Ok, that’s an exaggeration, I have a 5 gallon plastic bucket of this stuff that I rinse all my other equipment with. I put it into spray bottles and squirt everything my brews are likely to come into contact with. One bucket of Star San lasts me well over a year – and that’s one capful!