S&W introduced the 357 Magnum cartridge in what collectors call the "Registered Magnum." These were made 1935-39 and were the top of line, deluxe, custom ordered revolver. From 1939-41 they are called "Pre-War Magnums" as the registration of owner to gun by S&W was dropped.
Production resumed after WW II in 1949 with the newly designed "short action" revolver that S&W simply called "The 357." In 1957 this model was designated the Model 27. In 1961 an engineering change made it the 27-1. It became the 27-2 in 1962. Since the 27-1 was made only one year collectors seek them and prices run high.
The 27-2 was made until 1981. From 1962 until 1970 the serials carried a letter S prefix. This became an N in 1970. If you hear "S series" it means it was made 1962-70 and has the S prefix. Up until 1968 S&Ws came with "diamond stocks." These had a small diamond of uncheckered area around the screw. The small Magna style stock was standard on 27s until 1974 or 75 when S&W decided all 27s should come with full target options (wide trigger, wide hammer, big target style stocks). IMO a mistake on the 3.5" guns.
Usual barrel lengths are 3.5, 4, 5, 6, 6.5 (rare), and 8&3/8 inches. Blue or nickel for finish. The 3.5" barrel was dropped in 1979 and replaced by the 4" so the 27-2 in 4" length was only made three years.
This is a 5" nickel M27 with "diamond" Magnas:
This is a nickel 27-2 with the 8&3/8" barrel and the 1968-1981 "football" targets. It also has the Patridge front sight (not partridge) found on the vast majority of 27s with 6" or longer barrels:
This is a blue "357" (or "Pre-27" as often called) from 1956 wearing period non-relieved (no speed loader cut-out) target stocks. The 6.5" barrel with a ramp sight is fairly uncommon:
A 3.5" 27-2 wearing post 1968 Magnas. This barrel length is far and away the most sought after.
There, you now know pretty much all you need to choose a 27 for shooting. Any will work as a shooter, but bear in mind that the older the gun is, and the shorter the barrel gets, the higher the price goes. Good luck