There are lots of ways this could be done, ranging from hand tools to big-time, heavy-duty machinery (Aside: In the Owning/Operating section, there is a thread on "Bush Hogging the forest". I think a forestry mulcher would be great for this application, ie, when the trees get above 3" or 4" in dia, where a regular bush hog or flail mower would struggle.) I suspect a bush hog might be problematic both because some of the trees are kind of large and because you want to maneuver around some larger ones; I haven't found a bush hog to be a precision instrument. There are lots of toys, er tools, available that might help. Mowers/flails, tree shears, Piranha tooth bar, grapple rake, ratchet rake all have their uses depending on the size and accessibility of the shrubbery.
Unless you want to pay for equipment able to handle the biggest of the material you want to remove, it will take some maneuvering and implement switching to get the job done; the flexibility of a skid-steer with a mulching head would make this easier, but it might not be the cheapest way to go.
Finally, when you say "fence line" do you mean there is actually a fence there (there are lots of threads on wrapping fence wire in equipment!). I'd hate to run a chainsaw, mower, flail or mulcher into a wire fence.
Bob