I have a 63, and am very happy with it. But, if I was looking for just one S&W 22lr revolver, I'd get a k-frame. 617s are hard to find, but good used 17s abound, and are cheaper than a new 617 (and handier IMO).
That being said, my shooting buddy is in love with his 63, and wouldn't give it up for any other 22lr. Snub nose 22lrs have never appealed to me, so I cannot comment on the 317. All j-frames, IMO, need a trigger job to be more than just functional self defense weapons.