Alright, there's a lot of varying answers, but I'm not seeing a few big and important questions being asked. Is your truck 2wd, or 4x4? how many miles on it? Your first thing to do, is get the front end off the ground, and see if anything feels loose when you try rocking the wheel up and down, as well as side to side. Then, if you feel movement, it'll be a little tricky, but you'll need to determine what is causing said movement. Another item not mentioned is improperly balanced tires. This can also compound your issues. As can very badly worn and cupped tires that can create and amplify a lot of vibrations.
The caster shims are great, but that's something that REQUIRES an alignment immediately, as every change to camber/caster (and they do change both) also changes the toe angle of the tire.
I want you to understand, this isn't rocket science, but it CAN get complicated and stabilizers aren't a fix at all. I owned a Jeep on 36's and deleted my stabilizer entirely. I didn't feel even a HINT of difference. Not one. They're honestly not useful at all. That's money better spent on diagnosing the issue, and fixing it. Not putting a bandaid on it.