I am interested in buying an older used 30-06. I have seen rifles with the iron target sights for $125. I wonder if they will shoot. Looks are unimportant for my uses. So, what should I be looking for in a used rifle that will preform well enough for varmit and deer?

Remove the bolt and look in the bore for pits, scarfs and wear. Check the firing pin for bluntness (wear), overly enlarged firing pin hole and bolt face for gas erosion. See how tight the bolt and action lock up. Look at the muzzle for wear or nicks/gouges. If possible, look alongside the barrel from the rear to see if you detect any alignment problems. If the store has them, try a dummy round in the chamber and release the trigger to see how hard the firing pin hits and if there's any excess creep or backlash to the trigger.

For $125, you're not going to get a pristine center fire rifle - if possible, buy with the stipulation of return when you have a gunsmith check out the chamber with go - no go - field guages and he finds something major wrong with it.

kdub:
Good advise.

You can get a little more anal and check the muzzle crown by taking a Q-tip and running it around the crown.
Look for "fuzz" that will stick to the crown if it has been damaged.
There shouldn't be any fuzz sticking to the crown.

Sometimes it's hard to tell if a crowns been damaged and this method will detect damage that the naked eye may not.
Cheap too.