Where to live in Cambridge will depend largely on your budget. As your husband is a postgrad, will the college or the university accommodation office be helping you find somewhere?
It's a long time since I was living in Cambridge, and that was as a student so before I had children, but I used to live around the Mill Rd area (not far from St Matthew's primary at one stage) and I think it would be quite a convenient area to live with children, and it is easy cycling distance to St John's and most of the university faculties. Chesterton, an area just to the north of the town centre, might also be worth looking at - but I expect some current residents of Cambridge might be able to give better advice.
As far as schools go, again I can't comment on specific Cambridge schools, but I was also in the position of moving to the UK with primary school aged children, and I can say that it will probably be no easy task finding places for all your children at one school to start in September.
It will depend on which schools have empty spaces at the time, and the chances of finding a good school with spaces in (I guess) year 5, year 2 and reception classes would be quite low (if you give us the year & month your children were born, we can tell you which school year they would be - it's not the same as theUS, which I presume is where you're from?)
Priority in waiting lists for school places usually depends on how close you live to the school, and also once you have one child there, siblings also get higher priority, so you might need to take a place for one child and continue home educating the other two until a place comes up.
There are strict limits on class sizes in reception, year one and year two, which makes it harder. I would guess that as Cambridge has quite a mobile population of academics, places do come up, but the reception classes are likely to be very full.
As far as religion is concerned, it is possible to avoid church-affiliated schools, but even non-religious state schools in the UK all cover the same religious education syllabus, which covers Christianity and the other main world religions, and they are all obliged to carry out a 'daily act of collective worship of a broadly Christian nature', which in most cases basically means singing some vaguely religious songs and maybe saying the odd prayer in daily assembly. The local vicar may sometimes come in to lead assemblies.
Most schools also pay some attention to the main festivals of other main religions, so they may light candles at Diwali or do something special for Eid etc. Parents have the right to withdraw children from assemblies and RE lessons if they wish, but very few bother (I'm an atheist, and I did not withdraw my children).
Hope that helps as a start, and I hope someone comes along who can be more helpful on Cambridge specifics.