Trying to get a proper 3gun shotgun done for $500 is going to be futile.
Only option there is to go pump action with a used model 870 or 500, then upgrade it. You WILL hate the pump gun after a few matches, and won't have much value in it to trade towards a proper semiauto. I ran an 870 for a while, bought an 1187 eventually, then an M1S90. Gave it up a few years ago, maybe stage design has moved COF's in a way to level the field between autos and pumps, but I highly doubt that. I would personally buy an M4 today (hard to pass on the M2 3gun from last year), but the M2 has a lot of favor in 3G.
The only guys that ran pump guns, when I was playing, were either new guys that couldn't afford autos, or LEO's that were running their duty weapons (usually 870's) as a means for "practice how you play" training.
1187 or M2 are the way to go, no matter how long it takes to save up for them. Versamax or M4 also good options. Have heard of guys running Saiga 12's, but that definitely wouldn't be my style.
If you're just out to have fun with it and not at all concerned with time, then grab up an 870, 500, or Supernova. Anything you can swap barrels in a hurry with if you'll be field hunting and 3 gunning with it. I use an 18.5" Carlson's after market barrel on one of my Supernova's for coyote calling, could swap back to the factory 26" barrel in a matter of 2minutes for waterfowling.
Maybe there's some Stoeger or Franchi with parts compatibility but lower grade finish that would get you there. I have heard, but don't know it to be true, that the Stoeger 2000 is basically a low grade M2 with 80% parts compatibility. Might look into that.
Very likely that your best option will be a used 3gun shotty. At least that way you're buying something that's ready to go, rather than buying something for about the same price, then spending money to convert it over. Puts the monetary loss of conversion cap-ex on the last guy.
