It's a small village, without a whole lot else there. Also on the wrong side of Cambridge for things like St John's, and many university departments (be aware that there's no such thing as 'the university' - it's a collection of colleges, departments, and other buildings located in various parts of town, although mostly pretty central/west). Postgraduates need permission to have a car (though with a reason to have one, like a family, this would normally be granted, but you'd have to show that you could find somewhere to keep/park it). For many postgrads, there are also residence rules about how close to the centre of Cambridge you have to live, although again I suspect that with a family, exceptions can be made. St John's is generally very good about finding accommodation for students, including postgrads, and would likely have things like flats etc available - have you checked with them yet? They are often quite central, and much more affordable than private marking renting.
Village schools out that direction are often oversubscribed, so you might not be able to get any/all of the children in to the local school, and in that case, you might be sent to wherever the next nearest one with places is, which might be some distance (transport provided if it's far enough away). They might not all be at the same one, either. At least in the city, the possible schools would be closer - you still are at the mercy of finding one that has all the places that you need, but the alternatives might be closer to each other. Living in the catchments won't help you get a place intially, if there isn't one - if a place (or three) comes up at the schools you want, you can apply for it wherever you are living in the city. So you don't need to live near, eg., St Matthews, to get the places there. I imagine you'd be wanting to look at primaries that are at least two-form intake, or more, if you want to get all three children together.
The commute from the villages on the east would not be pleasant, and I doubt that 20 min is at all realistic at rush hour times, especially as you'd also be crossing the city. The A14 or the Newmarket Road, which you'd take, are often very congested, and the time taken to cross the city from there would add a lot to the journey. There is a park and ride on the newmarket road though, so your husband would possibly want to drive there and take the bus into town.
All the small villages will be seen as safe, I'm sure.
I think the C of E affiliated schools in the villages out that way are moderately religious, but I am not sure.
Other villages more to the west might be more convenient - Histon, Girton, Barton, Trumpington, etc etc. Even ones to south like Shelford, Sawston etc might be doable, though longer. Any commute time that you calculate based on distance you'd have to seriously extend, based on traffic!! And again, you'd be unlikely to want to be driving in every day, so looking at bus routes would be good.