You have got a good big bore, and a carry gun in the 36-7. The L frames 357 are probably the most durable/practical of the 357s
So, while the model 19s are great guns, as are the model 15s and 14s, your not increasing your versatility much with one of those. Although a snub 19 or 15 are a even a model 10 would give you another carry option over the J frame, the only real advantage is 1 more round and in the case of the 19 a bit of a step up in power. The trade off for that 1 round is they are heavier and bulkier.
All that said, I would recommend a model 18 or 17. In the shooting world nothing improves your ability more than practice. This goes 3 fold for handgun shooting. You can buy 22lr way cheaper than 38 specials. Right now at SGAmmo you can get 5000 Winchester 22lr for $170 plus shipping. Thats a bit of shooting. You can't load 38 specials for that kind of money. Primers alone are almost 3 cents. Low cost, low recoil and noise trigger time. Shoot targets. find a spot in the hills, place small targets around, (ping pong balls, the little nylon slide boxes ammo comes in, pop cans) walk around shooting at different ranges and angles. Single action, double action. Please clean up after yourself. Ping pong balls are remarkably durable and move around great, so you have to follow them with your gun. If you can bounce one with every shot in a cylinder your doing great. No rabbit is safe from you and your K22. Fried Cottontail, Yummy.
A model 18 and a lot of bricks of 22lr did more for my shooting than any other gun.