Phenomenal post by
BLUEDOT37 but then again, if you hang out around here, you've come to expect that!
I'll make just one slight correction and add a small take...
Can anyone give me some more info on this gun? I don't know much about s&w semi autos or their naming convention. Is this frame shared by other guns?
Would I struggle to find spare parts for this gun?
Basically I don't want to buy a paperweight
This model was released in 1993 and I have argued in the past (and will again!

) that outside of the freakishly limited full customs (that are almost literally NEVER seen) and arguably the Briley Comp (which I have never handled) that the
3566 Limited, when lined up against absolutely every other Performance Center pistol that that PC ever produced, could very be crowned
THE finest. And certainly not by a huge margin, but just by a bit.
This is to say that all the PC semiauto pistols are phenomenal, but the 5 and 6-inch "Limited" target guns are the best, and of those... the 3566 Limited may be the single finest.
This pistol does in fact share a frame with one other model, and that is the PPC-9. The PPC-9 came in a few different flavors, there was the two different 5-inch guns, one with the short dust cover and square muzzle, and the more plentiful and traditional one that looks much like the 3566 Limited. The PPC-9 was also offered with a 6-inch long slide and barrel, and the WISCHO Target Champion 9mm series was a re-named PPC-9 for the European market, these guns often had wood Nill stocks and a more traditional Bomar style rear sight where the PPC-9 has the "advanced" Aristocrat rear sight and taller front sight.
Would you struggle to find parts? Well... I can't imagine which parts we are talking about. I'll start this way... if you damage the gun or wear it out, then you certainly have a problem. S&W can't honestly help and as a hardcore, knee-deep enthusiast of these guns (these are the absolute center of my interest, bar none), I would investigate nearly any/every avenue before I even considered asking S&W for help. I personally believe that S&W wouldn't recognize this pistol if you shipped it to them, and I'll leave it at that.
These are my OPINIONS, and not being yelled out as fact.
If you broke a small internal part... let's say an ejector, extractor, magazine catch, etc etc... not a huge worry there as these are typical 3rd Gen parts (for the most part!) and a billion of these parts exist from many sources. (ugh, yes, even S&W has some)
If you damaged the frame the or barrel or the slide, you would be up the creek. You would need to investigate a true craftsman gunsmith and there would be a period of inspection and discussion before embarking on
ideas for a solution.
I am not the timid type. I would rather spend my money on a great old used gun and take the risk of a problem with no recourse than to purchase newly made junk. That's just me.
Will this gun be a paperweight? Well, you said it looks to be unfired. I have a 3566 Limited that was used in competition. I don't know how much, for how long, and I don't know if the guy who sold it to me bought it new or used. (I'm gonna ask him the next time I see him, he's a helluva nice guy!

) and I also have a 5-inch PPC-9 which is nearly but not exactly the same thing and that pistol has a documented
6,286 rounds through it minimum (it has more than that, but that number is certain minimum) and it shoots like a house afire, it is TIGHT, it's feel is INSPIRING, it's accuracy is FANTASTIC, it's trigger is SUBLIME and I could continue but I'll need to dig out a thesaurus.
What could you shoot in this pistol, as it is chambered for .356 TS&W, which is 9mm x 21.5mm...? Well, you could buy .356 TS&W brass and load your own, and this brass is available right now on Gunbroker. You could also buy new old stock .356 TS&W ammo, also to be found at the same place. 9x21 brass might work? As for handloading, I would not use standard 9x19 brass but we have another frequent poster here that will hopefully add his thoughts and suggestions as he has been there and done it. (poster
colt_saa)
As suggested by
BLUEDOT37, check out Scott Sullivan's Briley conversion barrels, also found on Gunbroker. You could put a 9x19 barrel in it, but I also agree with
BLUEDOT37 in that I'm not sure about the best way to make sure it fits as perfectly as the original.
To wrap this up:
It is my opinion that if you purchased a nearly new or mint or possibly unfired
3566 Limited, you might be purchasing one of the absolute finest semi-auto pistols that Smith & Wesson ever made, ever, truly
ever.
I cannot imagine any situation where that is a paperweight and if you do buy it and it troubles you, go ahead and send me a PM and we'll talk money. For the right money, I'd love to have another.