These calibers will be useful for scrounging ammo:
22 long rifle: Very, very common, so easy to find. Added benefit is that bullets are tiny so you can carry and store more of these than any other caliber. Much, much more. And they are about the cheapest of all ammo to buy. They are good for small game but they are also lethal enough to disable and kill humans. Can be used in rifles and pistols.
357 magnum: A 357 pistol will also fire 38 ammo. So with this weapon you have two very common types of ammo you can scrounge and use it for one gun. Also, to make it easy on you is that you can get ‘lever action rifles’ that also shoot 357 and these rifles are about the lightest weight rifle you can possibly get and also they are very reliable. This is not the best rifle ammo but it will do.
223 ammo which is used by the US military. This caliber is common in the US and tons and tons of it gets sold as surplus so it is fairly cheap compared to most other rifle calibers. The rifle to get is a Ruger Mini 14. This rifle is as reliable and durable as you can possibly get in it’s caliber range and is fairly lightweight for carrying. Also, parts for this very common rifle should be easier to scrounge than most any other rifles. This military style rifle is excellent for self defense.
12 gauge shotgun is the most common size of all shotgun ammo and will be your best bet for scrounging shotgun ammo. The shotgun has a very wide range of ammo types so it can be used for hunting the smallest of animals up to the largest.
9mm pistol ammo is also very common. No so great for anything but shooting people. Like the 357 mentioned above this can also be found in lever action rifles. But I consider this an inferior caliber to 357 for the purpose you seek.
You didn’t ask but I’ll mention that for ease of maintenance and ruggedness and reliability that revolvers are superior to automatic pistols.