You don't need to worry so much about doing damage. Reloading is pretty forgiving of most mistakes. It's pretty hard, but not impossible, to damage a firearm with handloads (especially a .308 bolt gun or a .44 mag. revolver). Just follow the manual and take things one step at a time. You'll be fine. If you have a class or can get an experienced handloader to help you, by all means do so. However, you can learn it on your own. Feel free to e-me if you have any questions.
I prefer RCBS equipment and dies. The kit that includes the Rockchucker press is an excellent value. It has everything you will need to get started, except dies and components. Lee is cheaper, but you get what you pay for (no flames, please).
There is nothing wrong with buying factory ammo and then reloading the cases. However, it looks like you want something that factory ammo won't do. So why not spend your money on getting started shooting the ammo that you want from the git-go.
Brass life depends mostly on the firearm and the way cases are sized during reloading. On modern commercial firearms, the chambers are such that brass life tends to be good. Read up on the Web regarding how to neck-size rifle cases to extend brass life. For your purposes, pretty much any brass will do. Norma and Lapua make, IMHO, the best rifle brass. However, I would recommend something economical like surplus military cases for the .308 and Winchester, Remington, or Starline for the .44 mag. See how many firings you get out of them. If they last (and they probably will), you really don't need to spend the extra on expensive cases. I don't advocate picking up range brass. You don't know how many times it has been fired, nor what else it has been subjected to. Brass is cheap. Much cheaper than your gun or your body. So, why pick up range brass?
Once-fired military cases are cheap and typically last many firings. Military cases tend to have thicker walls than commercial cases, however, both are uniform from case-to-case. You just want to be careful not to develop maximum pressure loads in commercial cases and then load the same charges into military cases. Because of the thicker walls, the military cases' internal capacity is less. Consequently, the same charge will produce higher pressures in military cases. You'll be fine as long as you work up loads gradually in whatever cases you are using (which is what the manual will tell you to do anyway).
The two things that you look for to determine whether the case should be reloaded again are: 1) neck splits 2) incipient case head separation (weakening of the case head). A neck split is a vertical crack, usually near the case mouth. This is obvious and can be seen with the naked eye. An incipient case head separation can sometimes be seen, but your objective is to feel it before you can see it. Each time the case is fired and then resized, brass migrates from the head (base) toward the mouth. Eventually, a thin horizontal band develops about 1/4 inch up from the bottom. You can feel this by dragging a wire with a small "L" bent at the end (a large paperclip will do) upward along the inside of the case. If a thinned band is present, you will feel the wire "drag" as it catches in the thinned band. When you can feel the thinned band, toss the whole lot of cases. If the head gets thin enough, a bright band will appear on the outside of the case. This means that you have already gone at least one firing too many. If you keep on firing the case, it will eventually crack through and the case head can separate (blow off). A case head separation can do damage to the rifle and blow hot gases and other nasty stuff in your face. However, you will never have a problem if you follow the manual and check your cases. Here's a pic of one that almost let go. A crack is visible on the outside of the case. You never want to see this: