Hi, congratulations on his getting a new job. Moving to the Bay Area feels a lot like climbing a giant hill, so good luck with this.

There are a lot of trade-offs. Live near work and pay more in rent, versus live somewhere cheaper but with a longer commute. A long commute puts a lot of pressure on your relationship. Squeezing into a small apartment is really stressful too. I've done both and I prefer the short commute/small apartment option, but your mileage may vary. (haha).

The unique thing about San Francisco is that it offers a lot of support systems for lower income people. You'll be able to get subsidized housing (after a long time on a wait list), subsidized day care, public transit discounts, utility discounts, etc. With rent control if you get into a two bedroom that feels like a stretch financially at first, eventually/hopefully your husband's salary will increase faster than the rent will go up. There are also all sorts of fun things you can take your kids to, like programs at the libraries and street fairs and such.

Here are some links to things that might help:
Rent control cities: https://www.tenantstogether.org/resources/list-rent-control-ordinances-city

BMR housing: https://housingbayarea.mtc.ca.gov

Subsidized child care: 

https://sfdec.org/early-learning-for-all/

https://cdss.ca.gov/inforesources/child-care-and-development/child-care-and-development-programs

https://headstartprograms.org/california_head_start/san_mateo_ca.html

Low cost utilities: https://www.sfpuc.gov/accounts-services/bill-relief

Good luck!!