How much do you want to spend, what’s your rough percentage split tarmac/trail and what are the trails like in diffreent seasons – will you run on them year round…?
That’s then your start point for deciding which shoes might fit the bill. Personally, I have Inov8 Trailroc 245 for trail running and will wear them year round, split 20/80% tarmac trail on generally well-draining hard packed or loamy trails with some mud in the autumn/winter; alternatively, I have La Sportiva CRosslites for the fells, split 5/95 at most and ranging from dry, rocky Lakes to boggy Peak in summer, snow in winter.
If you’re going for more road than trail you could go for anything from Adidas Kanadia, or similar, to something like the Inov8 F series. It all depends on the bias of tarmac v trail how aggressive a sole you go for, but you probably really don’t need a proper fell shoe as, aside from anything, they’re not fun running on tarmac and you’ll wear them out in no time.