I also have and use a Mossberg 935 fully rifled for deer hunting, but it's a tank.
The 20 gauge is like a toy ( weight wise ) compared to the Mossberg.
But boy does my Mossberg 935 shoot good.

Look for an old smooth bore single shot. The guns made in the 30's and 40's had thicker tubes. I have a scope on mine and it is very accurate. I built a 20 gauge rifled gun but my buddy uses it. He hunts more fields than I do and swears by it. If you hunt wooded and thick areas, you can not go wrong with a smooth bore for price and performance. An old single shot can be bought for $30 and up. Stay away from the newer ones, the tubes are thinner and sometimes they will not deal with slugs well. An added bonus is the shells are really cheap too.

I agree with the Mossberg guys, good guns, decent price, and will take a beating.Brother and dad both got the combos with slug barrels and smoothbores.Brothers slug barrel shoots like a dream, dads never did shoot slugs well, took it off and just shot slugs through the smoothbore, it put them right in where you were aiming.

My Mossberg 500 came with a smoothbore slug barrel with rifle sights. It shoots rifled slugs out to 75 yards with good accuracy. If I wanted a slug gun just to get me into the woods for relatively "cheap", I'd probably go this way. As stated before, rifled slugs are cheap and they do hammer deer.

If you are just shopping around trying to find a good deal on something, I'd be looking for a used Savage bolt action. Quite a few folks buy these and then deceide they don't like the recoil of high performance sabot slugs.