I'd be real clear in your mind how you want to use it, then pick the details from there.
Probably the cheapest way into a 20 gauge is to pick up a used GM drop-n barrel in 62 cal smoothbore. GM doesn't make them any more, but they pop up now and then used in the $200-$250 range.
They're 1", so I dropped mine into a TC Hawken stock. Ick. Fine for shooting RB, but that hooked butt was problematic for quick shooting with shot. Moved it to a Renegade stock, and it was better for shot, but the sights were kinda in the way for me. Worse yet, it's kind of a crowbar weight and balance-wise for wing shooting or quick rabbits.
If you're looking to do both, I'd go for a "fowler" design. If you're looking mostly at shot, I'd go for a SxS or a light single barrel if you can find one.