I don't live in Geneva but work there and live across the border so know a little.
Schooling options depend on whether you are going to stay or if it is a long term posting. Swiss state schools start at 5, in French, but a lot of expats send their kids to private international schools. Some are based on the UK system, some on the international bac (through English, French or both). Private schools are expensive and the company generally pays most if not all of the fees (c. 10k...). What you choose will depend on your situation.
The Swiss system is NOT set up for working mums. In Geneva, I am told childcare is expensive and hard to find with long waiting lists. The availability of jobs will depend on your experience and what you want to do - unless you have fluent French, you will be restricted to the international companies and competition is high but there are 50% posts advertised. Geneva is a who you know kind of city so personal contacts will be a help: ask people you know or meet to tell you of internal posts.
Can't help you with the apartment prices, but living across the border in France is generally MUCH cheaper and much better in terms of childcare availabilty. I do know colleagues have thought they were coming to Geneva on a great wage and then discovered the cost of renting. Also, there is very little occupancy in the city so finding a place to live can be difficult - be sure to ask if you get help with relocation and finding an appartment. Living in France can be a long commute if you work in the international sector and live the other side of the lake but you will get a lot more space. Try around Ferney Voltaire etc. Geneva does have good parks for kids and in the summer is lovely but in the winter activities in the city are limited.
It's a fantastic region to live in I have to say but do make sure the package is a good one as it is an expensive place.