slug gun
I have owned a few slug guns, and each one had its plusses and minuses. I presently own a Mossberg 500, with an aftermarket rifled slug barrel with cantilever scope mount. It shoots very good groups, but recoil is a little stiff. With an aftermarket Limbsaver pad, it works great.
I have also owned a H&R Ultra Slugger single action which was a good shooter but very heavy. I also owned a Mossberg 695 bolt action slug gun (it was OK, but not my cup of tea). Lastly, I owned a Remington 1100 with smoothbore slug barrel. Groups were only fair at best.
To me, a good pump shotgun with a rifled slug barrel is about perfect. You can then use the regular barrel when you need, then switch out to the slug barrel when you need that. Mossberg (500), Remington (870), Ithaca, and Browning all have aftermarket slug barrels. However, research this in detail first. Some barrels are more expensive than others. My Mossberg shotgun cost me $200. The slug barrel was another $75. So, for $275 I have a double duty shotgun that I can use for ducks or doves, home defense, or deer hunting with slugs, with just the change of a barrel. With the cantilever scope mount, the scope is attached to the barrel, so you never have to resight it (aside from an annual recheck).
As far as the 12 vs 20 debate. A 20 gauge will do fine for deer, but I honestly believe a 12 gauge is better. If you are small framed, then a 12 gauge may be a little much, but if you are medium to large framed, it won't be too bad. Extended range sessions can be gruelling with either one.
I hope this helps.
Todd