A common piece of advice that we kept on hearing from Americans that have been in Israel for a number of years (here is the gist of it, heard from a few different people): it is very important to speak English at home to the children. Not only that – one must take care to have your children answer you back in English as well.
Kids will definately learn to speak Hebrew fluently. It will be their mother tongue. If you do not speak English at home, your kids will not know English beyond the meager level that they learn in school. If you do not make them talk in English, they will never learn how to speak it (just how to listen to it).
What is wrong with this? Well, unless your parents understand and speak fluent Hebrew, your children will never really be able to communicate well with their grandparents. And as immigrant parents (yikes), the same thing can end up happening to you (unless you go to ulpan like a good American oleh). Additionally, in today’s world, fluency in English is one of the most useful ways you can prepare your children to do business in a world where English is the dominant language.
I heard from one person (who made aliyah a couple of decades ago): “the biggest mistake that I ever made was to not make my kids speak English at home)”. I had not thought about this issue so much until three or four people mantioned it to me over the course of one Shabbat. Something to think about…