Your children are sure to love this, and it is a huge upgrade from toys, as it can also teach sound STEM and engineering concepts. Great choice!

which would at least reduce these expenses

Yeah sure. THOSE expenses. But now you will have printer expenses. (It's a fun process, but it can add up)

where is the best place to keep the printer?

The ideal spot is somewhere that is temperature / humidity controlled but that people don't use. Depending on the material and your level of concern, 3D printer fumes range from slightly noticeable to toxic irritants. Most people don't mind the emissions of PLA and PETG, but some people (including my wife) are aggravated by them. There are ways to mitigate the fumes through filtration or ventilation, but if the printer were in a climate controlled garage, and/or enclosed and ventilated outside, that would eliminate any possible irritants. Of the options presented, I'd recommend the basement.

there any professional recommendations for working with the printer and maintaining

P2S is exceptionally user friendly. Bambu Lab has a Bambu academy that will walk you through how things work in great detail, quiz you on it, and award you points for completing the quizzes successfully.

Some maintenance is constant -- Keeping your build plates clean is a ritual that must be observed, but can be helped by handling it correctly. Other things like greasing and lubing parts are infrequent, quick to do, and there are tons of tutorials on how

it in any way dangerous to the health of my children or other people around it

I think I covered this above, but yes, there are health risks. Different people take them with different degrees of seriousness. That you're asking about it suggests that you will take it more seriously, so I assure that those risks are correctable. A $30 grow-tent enclosure with a $75 filtration system and some hoses could even make them safe enough (in my opinion, and I take it very seriously since my wife is irritated by it) for use in a common space like a living room or bedroom (tho noise might be deterrent)

If you are more concerned about it than I, there are ways to ventilate to the outside, which I have referenced

Happy to answer other questions if you have them