it has to go fairly near your incoming water supply, and a drain for when it is regenerating and rinsing itself.
When full of water and salt it will be heavy, so it ,ight be placed inside a litchen cabninet but standing on the room floor, not the bottom of the cabinet.
Larger ones are usually taller but not fatter. A larger one can hold more salt and will go for longer without needing to be refilled. It also has a larger cylinder so needs less frequent regeneration. The bags of salt can be quite heavy if you have to tip them in, but you can get smaller bags or rectangular blocks, which work out more expensive.
Mine is in the garage and goes a couple of months between salt fills. I use the sacks. Never collect salt in your own car because the tiniest spillage will rust a hole in it. Look inside the salt delivery van and you will be shocked.
If your kitchen has a plumbing duct in the corner, see if you can fit it there. There is often a dead space. You will need access. In mine the dishwasher rolls out on a wheeled base, bringing a section of worktop with it, for access to the plumbing. A chippy or kitchen fitter will be able to devise a way. You might consider countertop flap hinges, as used in bars.
I'd ask around for a local softener company (there will be one) who offers repairs, sales and salt deliveries.
The first week you get one, you will be amazed at how foamy your washing machine is, and how little soap, conditioner, shampoo you need. The second week you will be astonished how soft your towels, hair and skin are.