For myself a HUGE part of why I have my handguns is for the sporting competitions. Shooting bullseye is OK now and then and I do enjoy it for the focusing on accuracy that it provides. But the handgun activity that puts a really big silly "kid with a big ice cream cone" look on my face is when I'm using my handguns in one of the speed shooting style competitions.
So before you say that you won't use your handguns very often I'd urge you to at least attend some of the matches for various styles of competition in your area. See if there's something that clicks perhaps.
And now onto the guns themselves.
Folks already mentioned the S&W 686. It fits your desire for stainless and it is a premium choice for use in some of the competition classes for revolver. Only a half step below the S&W, IMO, is a Ruger GP100. I simply prefer the trigger on the S&W more than the Ruger.
For a semi auto you're really limiting your options by insisting on stainless steel. There's many great shooting and great feeling guns that don't come in stainless. In 9mm the Browning Hi Power comes to mind. And for 1911's there's many great makes and models that again are only in blued steel. If this gun will be primarily a shoot seldom sort of gun I'd go for one of these options. These are pretty much the two classic handguns that have the most history.
But if you go look at some of the matches in your area and decide to give it a try then the handgun will become more of a tool than an ornament. Now you can consider giving up historical appeal and focus on function. That opens up the options a LOT. There's the Glock mentioned above.... someone ALWAYS mentions the Glock

. And there's a host of other options. I find that the CZ's I use for such shooting are amazing tools. I use a Shadow for IPSC and an older pre-B style 75 for IDPA. Both weld to my hand like I was born with them and both shoot amazingly accurately when shot slowly for bullseye. And both work well at the speeds I shoot in matches for rapid fire.
There's no doubt that a 1911 and a Hi Power CAN be used for such matches but the single action only can force you into a category that you may not want to enter. On the other hand ANY collection that includes handguns should have at least one, if not both, of these classics. From there you can add the more practical "tools" for competitions. And even if you're bumped to a somewhat higher category by their use at least the Hi Power or 1911 will get your feet in through the door and you can get a taste of what gunning while running is all about.
And finally, if you do forego the idea of entering in speed related competitions and ONLY buy one each to round out your collection I strongly urge you to include a single action revolver as well. And for the difference it offers and the peak back at the guns of the old west I suggest a Uberti or Pietta over the Ruger NM Vaquero. The Ruger is a lovely gun. But the action doesn't use the "proper" design any longer. The Italian clones are actually faithful copies of the original 1873 style action. And for me that's a part of their appeal. But if the idea of stainless over blued has you trapped fully then a stainless Vaquero would not be a bad way to go.