Bent rims are a hazard of off-roading, potholes, and banging into curbs. Pneumatic tire changers can easily bend a rim if the person doing the job doesn't watch what they're doing. Personally I don't believe in trying to straighten a rim unless it's a ding in the lip. Once the metal has been bent it's been stressed. To bend it back will stress it some more creating a, however mild, weak point.
So, I want straight, new if necessary, rims on the front. A very slight off-center wobble in the rear rims should not pose a problem.
The best way to prevent the rims from being distorted on a pneumatic tire changer is to do it manually. It really isn't that hard. Two tire irons will do it. Just be careful of pinching the tube. Also remember to fully inflate the tire, and then let all the air back out, to let the tube seat itself within the tire, then inflate it again.
This is the type of tire iron I use. That little notch is great for hooking over the lip while prying the tire onto the rim.

I probably should also mention how to break the bead on these old wheels/tires. Remove the valve stem and let all the air out. Get your bottle jack. If you have a pickup, go get it. If not, ask a friend. Slide the wheel under the vehicle. Set the base of the bottle jack on top of the tire sidewall as close to the rim as you can get. Adjust the jack up against the frame of the truck. Now start jacking. As the base of the jack starts to apply pressure to the bead double check that it's
not pushing on the rim. It might take a bit of practice until you figure out at what point will the jack start to slide. Stop jacking before it slides over. Let it sit for a while. If it doesn't break loose, do it again at a different location around the tire. Eventually it will break loose.
Once the tire beads on both sides are broken free it's time to pry the tire off. Stand on the tire to push the sidewall down and hook the bar between the tire and wheel on the side away from your foot. Now pull on the bar until the bead comes above the rim. Stand on the bar and insert the second bar about 10" or so away from the first and repeat. Once the bead between the bars is up and over the lip of the rim remove one of the bars and continue to work your way around the rim. Once the top bead is completely over the rim reach inside and remove the tube.
With the tube out use the bars to leverage the other bead up and over the rim. There ya go, piece of cake! �;)
At this point I usually use a drill powered wire brush to clean the inside of the lip, If the rim is all rusty I will wire brush the entire interior until clean. Do not paint the inside.
One recommendation, do not reuse old tubes, it's not worth it. After what you just went through the last thing you need is for a tube failure inside your new tires.
Larry