Best to go to Charmouth and there is a free visitor centre there. Watch the film and it explains what to look for on the beach. You can hire a hammer and goggles in the fossil shop. Cafe at Charmouth beach as well. I have also been on a fossil walk in Lyme. It was very interesting but difficult underfoot with huge rocks to transverse and you need to wear walking boots and booking is essential.
Charmouth is a lot more satisfying for children as they can find fossils really easily. It isn't far to Lyme so you could go there for lunch (really fab place called The Bakery, I think, that we go to) and a look in the fossil ships/museums.
We went to Charmouth today and had a lovely time on the fossil hunt .
The heritage centre start with a family friendly 20 min chat on what to look for and what not to do. They even gave us a 5 min toilet / snack stop before we headed off down the beach. The group leaders have geological hammers so you don't need your own kit. I don't think many people found big fossils, but we all found a few little bits.
Suggestions - Get your kids to take a small bag to keep their haul in. And rummaging through rocks, pebbles and clay-y sand trashes your nails, I had to set to work with a nail brush and emery board when we got home.