We love living in Redwood City. It is one of the more affordable towns on the SF peninsula, has great weather and is centrally located so you can enjoy the many great things the bay area has to offer.
You should be able to find a house to rent quite easily. Rental markets are high right now but I think there is still a lot available. Your office will be directly linked to Woodside Rd/Hwy 84, which is surrounded by great neighborhoods West of El Camino Real (which is the main North/South thoroughfare for entire Peninsula). There are many conveniences and good schools in those neighborhoods as well.
For a 3+ bedroom, which is what I imagine you'd need at least, the minimum you should expect to pay would be $2,000 for a house. Obviously, the price can go much higher. There may be cheaper rents for condos/apartments. There are many small complexes in the area. I've lived in the area for a while now so I'm happy to have you message me if you want my opinion on anything specific.
My son is only 2 so I can't offer much in the way of schools but I know there are some goods ones and not so good ones. And a good amount of private/religious options.
Menlo Park to the South and San Carlos to the North are also great places to be and close to your office. You will pay more in rent for sure but might have access to better schools overall. (All these towns are very close to one another so even if you live in one, you are often eating/shopping etc in various adjacent towns.)
Woodside is a small, very wealthy community further West on Woodside Rd/Hwy 84. If you want a very affluent, small town feel with a great school that is still close to work, this is your place.
Like another mom said, you will find housing much cheaper across the bay in Fremont/Hayward etc but your commute will be longer and you will have bridges/tolls to deal with which have the worst traffic usually.
This sounds like a big move but I wish you lots of luck and hope you'll enjoy living here! Redwood City and the peninsula in general are very safe and family oriented with lots of things to do with kids of all ages.
Good luck!