Brita filter's do not contain BPA and are considered safe according to The Green Guide.
I personally use water straight from the tap, but our city water comes from a protected forest watershed and is very clean. You might want to contact your city water board to find out what contaminants you have in your tap water. If you live in the US, they are required by law to give you this information. Make sure your Brita filter removes these specific contaminants. If it doesn't, it is not doing you any good, and you should invest in a different filter.
Also, if you live in an older building, do not use hot water for cooking. Lead (that used to be used in pipes and pipe solder) is more likely to leach into hot water than cold. Before I fill a pot or the teakettle, I always let my cold water run a bit to make sure I'm using water hasn't been sitting in the pipes.
Do what you can to make your family safe, Mama, but don't drive yourself crazy over it. It just takes a little conscious effort to keep your family away from many harmful chemicals, and much of that can be accomplished by just keeping toxic cleaning supplies and bug poisons out of your house. Good luck!