The model 60 is a small frame (J-frame) 5-shot. The 13 / 65 is a medium frame (K-frame) 6-shot. Big difference in the pleasure of shooting! The J's are nice to slip in a pocket. The very best J in my view is the 642 with 1 7/8" barrel and completely internal hammer - you can pull this gun without any hangups and even shoot it through a coat pocket if you HAD to. Sealed hammer prevents any lint or gunk from collecting in the mechanism and no hanging up on clothing. These type of guns are designed for close range double action type shooting. They also require a lot of practice to shoot well! More than you might think!!! Lastly, they're not much fun to shoot. BUT... small enough to slip in your front jeans pocket or hold in your hand inside a coat pocket while you walk through dangerous places. And reliable.
For a gun which you will shoot more (and enjoy shooting!) go with the K-frame, 13, 19, 65, 66. The fixed sight versions (13, 65) are best for concealed carry... you don't need, nor want adjustable sights on a concealed carry defense gun.
Check pawn shops!!! And internet gun sales. Good luck.