I grew up with the full menagerie of usual pets as a child. I think any can be rewarding for a child. but realisitically they often turn into more of a chore. I don't think any small rodents (except perhaps rats, never had those) really enjoy human contact, if you work at it they'll happily tame enough to be held etc, but don't think they 'enjoy' peoples' company in the same way cats or dogs do. Plus to give them a good quality of life involves a lot more than people realise, in terms of cage size, enrichment etc.
Day to day, I think cats are pretty low maintenance compared to caged animals though obviously a much longer commitment, but that's what I'd pick over other pets personally. How old is your DC, that might change what suits them?
Kittens are normally easy enough to get hold of, and if you go for a rescue cat you could get a slightly older one and pick based on personality (bit of a gamble with a baby) - with a child maybe you want one that's a bit more chilled and cuddly, rather than an excitable always-wants-to-play cat?
They don't need much 'stuff', food, litter tray, some beds & toys they'll inevitably ignore in favour of random things they find round your house! Vets, I'd just ask around local friends for recommendations - Some are better than others with small or exotic pets, but if you got a cat any will be fine.
Insurance is the same as insuring anything really, an unnecessary expense, until it's necessary! I personally haven't insured mine but am aware that any illness or accident could potentially cost thousands so you do need to have some plan for that eventuality. Normal medical costs are vaccinations yearly, spaying/neutering/microchipping at first, and then worming/flea treatments etc.
You'll also have to consider what you do with pets if you go away etc. Caged animals would need someone to check food & water, cats would need the same, or possibly a cattery (this depends on how long you're away, what your cat prefers etc)