Absolutely Inov8. I have 5 pairs of their shoes at last count and have had others in the past ranging from absolute off-road fell running shoes through to the lightest smooth soled road shoes.
You will definitely find a pair to suit. I have an earlier version of the trailroc which is OK on hard packed gravelly surfaces and light mud, their new parkclaw seems to be aimed at you as well. Those are a decent compromise between grip in the mud and comfort on on-road sections for me.
The FLite 195 is my road running shoe.
If you are not used to low drop shoes, go very carefully to start with i.e. run a mile, no more, and build up very gradually. the Inov8 shoes have a system of chevrons on the back, denoting the heel-toe difference, more chevrons, more difference. I typically use one or no chevrons, so almost flat.