>>617820Start with short day hikes on easy trails with whatever gear you've got (maybe get some cheap fleece is all). Especially if the kids are young, they probably wouldn't be up to anything requiring more gear at the start anyway. Just bring water, snacks and a basic first aid/blister kit.
I don't really worry about clothes unless it's below freezing or wet, I hike in relaxed fit jeans all the time on nice days. If it is wet, then stick to wool or synthetics, but these don't have to be expensive.
Make it more fun for the kids by adding something besides just walking to the trip - like birdwatching, geocaching, catching minnows in a pond, collecting walnuts, or whatever.