I would recomend the late model 67 with the 2 piece barrel. I have a 620 with this barrel system and the accuracy is simply stunning, however as a 357 Magnum the bullet jump may degrade the accuracy a touch. With the 67 you get a dedicated 38 spl. so no bullet jump. As for the specific dash number, I believe that it's the 67-6 but could be wrong about that.
Now, the key to spotting the tensioned barrel is to look at the muzzle flange at the end of the barrel shroud. Take a look at one of the current Night Guards to see what that muzzle flange looks like. Also look for a recessed crown with the rifling ending about 1/8 inch into the barrel.
As for accuracy, IMO you can expect 1/2 inch or smaller groups at 50 yards if your up to it. I've managed some 1/2 inch cloverleafs with my 620 from a rest using a scope and feel a better shooter could do it for a full cylinder. Unfortunately, I tend to get over excited when I see just one hole in the target downrange and start throwing flyers.
Now, the 67 will only have a 4 inch barrel so IMO you will need the help of some optics. Fortunately, Bullseye competitions now allow the use of optical sights. If your eyesight is good enough to see a quarter at 50 yards I would recomend using a Reflex Sight. J P Rifles makes a reflex sight mount for their J Point reflex that sit's close to the bore axis and is quite compact. However, the J Point reflex doesn't have the clearest optics due to the use of an acrylic lens to minimize weight. As a result it's a reflex sight more suited to field use than precision shooting because the dot can be a bit fuzzy. However, J P rifles also offers an adapter plate for the Doctor Reflex that features a glass lens and excellent sharpness for the dot. Below is a link to my report on the J Point reflex showing it mounted to 3 of my revolvers, plus the good and bad about this particular sight. As for the Doctor Reflex, that sight can be a bit of a challenge to find. IIRC CDNN was selling the Doctor about 6 months ago, you may want to take a look and see if they are still selling it.
http://smith-wessonforum.com/lounge/155300-purchased-2-more-j-point-reflex-sights-range-report.html
Now for one final though on the reloading comments. If you are serious about getting deeply involved in Bullseye competitions I'd suggest that you have your revolver converted to run moon clips. Belows is a link to TK Customs who have had numerous rave reviews on this sight. Just something to look into. As someone with 2 revolvers set up for moon clips I can do nothing but rave about them, you just can't beat the convenience of having 150 or so rounds of ammo preloaded in clips ready to slide into the cylinder.
Now one final word on the 2 piece barrels. As far as I know ALL of them are ECM machined barrels. Which means they work great with jackted ammo but are a bit sensitive to leading when used with cast bullets. From what I've gleaned from this site lubrication is CRITICAL. If you plan on reloading, make sure you check for leading every 50 rounds expended until you figure out how to load for an ECM barrel. I'll also warn you to TOTALLY AVOID the Blaser aluminum hulled LRN, it's not lubricated at all and leaded horribly in my 620 the one time I tried it for 50 rounds. Took me 10 hours of work over 3 days to delead the barrel and the leading was so bad that if I had shot some jacketed ammo before cleaning the barrel I believe it would have either bulged the barrel or caused a full power squib. Yeah, the leading really was that bad.
PS; my go to ammo in my 620 is the American Eagle 130 gn FMJ. Accuracy is superb and it shoots very clean in my 620. However, the most accurate ammo I've ever shot in the 620 was some Speer Lawman 125 gn TMJ, that ammo yielded a few cloverleafs at 50 feet that I could cover completely with a dime. Unortunately, I haven't seen this particular Speer Lawman for sale in nearly 3 years. BTW, it was that Speer ammo that started me out on my quest to see just what my 620 could do and I've come to realize that I will never have the ability to shoot to it's full potential, best I've managed is some occasional 3 and 4 shot groups that keep driving me to try for 5. Now I considering dropping about 400 dollars on a scope with more magnification just to see if that will help. So, I'll warn you right now, if you get an exceptionally accurate handgun the quest to shoot it to it's full potential never ends.
PSS; I'll also admit that I have to cheat to get the results I've managed so far. Simple truth is I'm just not steady enough to shoot the 50 yard Bullseye course, so this old fart pulls a chair up to the bench and shoots from a sandbag using both hands.