I also wouldn't use gravel in the area for the BBQ, any food that is dropped would encourage pests and be very difficult to clean. It also needs to be level (fire on an uneven surface is never a good idea), if the area is very uneven, could you perhaps have some sort of terrace arrangement? Personally, I'd use stone or concrete paving slabs for the area directly around the BBQ, and if you're not that keen on stone slabs, decking, or something that's smooth and easily hosed down.
If you put gravel or something else down, you'll still need to put some sort of terrace in to retain it, otherwise you'll end up with mud at the top and a big pile of gravel at the bottom!
You don't need to dig up the grass (unless it's really nice turf you'd like to use elsewhere in your garden). If you don't want to keep the turf, I'd put weedkiller down, try and level the area as best you can, put weed supressing membrane down, and lay the patio on top of that (I'd do the weedkiller and some of the levelling and point my husband at the rest!!).
I wouldn't use gravel or loose stones or bark chippings in an area where food is going to be eaten (even though I have a dog that can catch food the little ones drop before it hits the floor). Just my opinion though.