In general, a 12ga is going to be more versatile than any other gauge, simply because of the amount and variety of ammo readily available. Due to the higher volume production of 12ga ammo, it will also tend to be less expensive.
As far as the 20ga vs. 12ga battle... if ALL ELSE IS EQUAL, then the 20ga should have less felt recoil, because they generally shoot a lighter shot charge (7/8 oz is normal for a 20ga... 1 1/8 or 1 oz are most used for 12ga). However, all else is rarely equal. 20ga guns tend to be built on smaller frames and are generally lighter. Depending upon how light the gun is made, recoil can feel more severe in a lightweight 20ga than a heavier 12ga.
Proper form and gun fit mitigate felt recoil to a large degree, as does a premium recoil pad (Pachmayar Decelerator, Kick-Eez or Limbsaver). Fixed-breech guns (think break-open guns like SxS, O/U and singles) do not do anything on their own to mitigate the recoil. Gas-operated autos will bleed off a portion of the gasses to cycle the bolt. This seems to delay the recoil impulse a bit and smooth it out... more like a shove than a punch.
It's been my experience that the type of gun requiring the most critical fit is an O/U. Likewise, I think the most accomodating type of gun is the autoloader. For those reasons, if I were recommending a gun for a new shooter (especially if they were planning on shooting sporting clays), I'd pick one of the following:
Beretta 391 Urika Sporting
Winchester SuperX-2
Remington 1100 Competition
I own and have shot the Beretta extensively. It's at the top of my list for a reason. The Remington is less $$$, but QC has been an issue for Remington for a little while. Used models can be found of all of them with a little looking.