You have an excellent philosophy.
As for which one to buy, let's break it down a little.
The J frame S&Ws are the small frames. They are lighter, smaller, and only hold 5 shots (in .38spl and .357mag). They are great for concealed carry, and can even be fun at the range but they are not really range guns.
K frames are the "duty" sized frame. They were carried by cops starting with the pre-model 10s (.38 hand ejector) that came out in 1899 and going all the way until most police agencies changed over to semi-auto in the 1980s and 90s. There is a reason they were the standard. They carry nicely, are heavy enough to be recoil friendly at the range, tend to be very accurate, and are overall nicely proportioned guns.
You could do a LOT worse than a K frame for a range gun. For range use, i'd think .38spl and adjustable sights might be nice, so I'd look for a Model 15 (blued), or Model 67(stainless). You can shoot .38spl in a .357mag, so also consider the Model 66 (stainless) and model 19 (blued). I have a model 19 that I adore. Probably not an issue for range usage, but don't shoot too many .357magnum loads with light bullets in any .357mag k frames. They aren't built for it and you can crack forcing cones. They will take endless amounts of .38spl though, and you're not likely to shoot much .357magnum for range use anyway so it's a non-issue, and do not take this to mean that K frames are weak. They are not. They can handle heavy bullet .357mag just fine.
The fix to the magnum issue (if you even want to call it that) in K frames, was the L frame. It's slightly beefier, and has many of the advantages of the K frame, but in a slightly stronger frame. They are newer, having been introduced in the 1980s, so you won't find one from the era that you're looking for, but if you see a nice older model 586 or 686, it's worth a good look. They are fantastic range and duty guns.
Next up, we have the N frames. They are the large frames. They are built for cartridges like the .44magnum and .45LC. Big thumper rounds. They are overbuilt for a .38//357.
The model 27 you saw fits into this category. The up side of them is that even with a diet of heavy loads, they will outlast you and your grandchildren. The weight also keeps recoil very minimal. The down side is that holding out all the weight in front of you can fatigue you during extended range sessions, and I find that they aren't as nimble or quick to the target as the K/L frame guns because of their weight. The weight is very steady, but the tradeoff is speed (at least for me).
Ultimately, it's really up to you obviously, but this is a very very basic primer. There are LOTS of models i did not mention and lots of info about each frame size that I left out. This is only the most basic of info to give you a springboard for your research. Get out there and snag a classic revolver, and when you do, take pictures, come back here, and brag about it. We want to hear how you do!
