First of all, take a breath. I get the impression that you’re relatively new if not to firearms then to revolvers at least. And, that’s okay. If that’s the case, you have apparently decided on a Smith & Wesson chambered in .357 Magnum, so I am confident that you have the good judgement to choose wisely.
Now, the list of revolvers that you mentioned covers a variety of frame sizes and as such, it covers a lot of different things that those revolvers are each better suited to do than others. You’ve got K, L, and N frame models on your list, so let’s break this down a bit. A K frame like the Model 66 you mentioned, is a medium framed model that is just about perfect for carrying. It is a fighting gun at heart with a long history of use by various well known entities whose job duties might sometimes include gun fighting. Both versions of the model 686 that you mention are only slightly larger in frame size, but that bit of difference makes them a very excellent choice for an all-around/general purpose revolver. The same gun you use for carry can be the one you hike/hunt with and it is at home doing any of those things. The 27 is a BIG gun. To put things into perspective, it is basically the same size as the famous Dirty Harry gun, but it’s chambered for a smaller cartridge than Clint Eastwood’s gun. And, while it CAN be carried, I certainly don’t recommend it as a daily CCW piece due to its size/weight. It is a gun best reserved for target shooting, and hunting applications with home defense being another role it might be great for.
Personally, I prefer my N frames to be chambered for either .41 Magnum or .44 Magnum, and would not consider one for a daily carry gun. And, while I love my older 66-3 2.5 inch as a carry gun, I kinda get the impression that you are looking at this potential purchase as something you might use to fill multiple roles for a while. If that is the case, I would strongly consider the model 686. There is a reason why it is such a wildly popular model, and if you select the barrel length carefully, I believe it could serve as your ONLY handgun until you’re ready/able to add to your collection.
If it were me, I’d look at the standard (non-plus) version, because I personally just like a traditional 6 shot revolver. Something about it makes me feel some connection to the past, and I don’t figure one additional round of ammo is going to see me through too many scenarios that I’ve failed to resolve with six. That’s just me though. I’d also look for an older model without the internal lock, but if a newer one appeals to you, and/or fits your budget best, there are plenty of people who are happy with them.
IF, you don’t intend to do any hunting, are not a big outdoorsman, and don’t see yourself being a high volume shooter expending a lot of ammo on a regular basis, I would go with a model 66 or perhaps a model 19. A K frame is in my opinion the best there is in terms of a dedicated carry gun. Again, I prefer older pre-lock models, but if you went with a new one I’m sure you’d be pleased.
As for barrel length, that’s up to you. If you will be using this revolver for a variety of tasks, I would normally say that a 4 inch would be about the sweet spot. However, since it sounds like you might be new to carrying a firearm, I think you’d find something a bit shorter in length and lighter in weight a bit less challenging, so I might suggest you go a little shorter if you can. If it is primarily a carry gun, for defense against people, I would go straight to a 2.5 or 2.75 inch barrel and never look back.
Good luck with your search, and keep us posted. Pics are mandatory once you’ve acquired your new revolver.