All the kittens we've had over the years have been around 8 weeks old, although the little girl we presently have - now 8 years old - whom we got via Cat's Protection, was quite poorly early on, had severe 'runs', and even our dear old female doggie was helping to lick her little bum - yeugh! - to try and help her.
We also took her to the vet but the condition gradually righted itself, and now she's a proverbial barrel on legs, whereas the little ginger tom we got at the same time has maintained his 'figure'.
The dirt trays are never that pleasant - understatement - but a little moggie will adapt to it very quickly - it's most unusual to have a 'dirty' cat, but it will have helped if it had its mum in its formative weeks to teach it how to groom itself etc.
After all, they're only babies, aren't they?
Good luck, anyway, Prudie. Hope you have many years of pleasure and love - on its terms - from whatever moggie you get?