I'm my own mechanic so take what I say with a grain of salt. Mine still shakes from time to time but nothing like it did when I got it.
I'd give the front suspension a thorough going over. Leaf springs will sag over time, and the bushings at the ends can go south, but before I replaced them I would check all the balljoints: pitman arm, idler arm, center link, tie rod ends (both ends of both tie rods). An easy check is to raise the front of the truck so the tires are off the ground and have someone move the tires back and forth while you check over the steering stuff.
Also make sure the power steering gear bolts are tight, and that the frame isn't bent or cracked where it mounts. This is a known issue on these trucks, and one that can be very dangerous if not caught in time. There are kits you can get to reinforce the frame there, or you can always make your own braces.
Other than the steering stuff, there's the A-arm bushings, wheel bearings, kingpins, and a few more parts I'm sure I am forgetting. If any of these parts are loose or bad, it can cause shaking and pulling, as well as tires(even if they look ok to the naked eye); different pressures in the front tires can cause pulling like you mentioned.