Several Good Choices.
J Frame Size:
LCR357 (Air Weight)
M&P 340 (Air Weight & Expensive)
K Frame Size:
2" & 3" 65
Snub Speed Six & Security Six Rugers
L Frame Size:
2-1/2" & 3" 686
Out of all the choices above the LCR 357 would be my first pick for CCW for a couple reasons. One it is barely light enough to pocket carry. And second it has a pined on front sight, so swapping the front sight out for something you can see like an XS 24/7 Tritium Night sight or a Fiber Optic is no problem to do. The Triggers are normally not terrible for factory. The polymer frame and Hogue Tamer Grip will really help with recoil.
Get a pocket holster such as a Mika, for pocket carry.
Get a Belt holster like a Lobo Model 1 or Enhanced Pancake. Have it Detail Boned and add an Inner Hammer Shield. The Inner Hammer Shield is a $5 Option, and will help to keep your shirt out of the holster, when reholstering.
My second choice would probably be the Ruger SP101 in 357 Magnum. They come in both 2-1/8" and 3" barrel lengths. Both lengths will work fine. The Steel SP101 is too heavy for pocket carry for me, and most who carry, so plan on a belt holster such as a Lobo Enhanced Pancake. The Original Old Model 357 SP101 will be market 125 Grain ONLY. It has a short cylinder. They are collectable and fairly rare but still encountered. The new ones will shoot 158 grain ammunition. Again the SP101 has a pinned on front sight, so you can again swap to an XS 24/7 or Fiber Optic front sight. For a reload you are a little limited. Safariland Comp I, HKS Twist Knob, Speed Strips, or a Jet Loader. I would probably give a 5 Shot J Frame Jet Loader a try.
I make Kydex Speed Loader Pouches mainly for competition shooting. However a Single Pouch for the Jet Loader would be the fastest reload possible with this revolver. I would give carrying a single infront of the holster a try.
My Third choice would probably be a S&W 65 in either 2" or 3" barrel length. They are fairly easy to find. Reasonably priced normally. The K Frame Snub is a very Shootable size revolver. For CCW Belt Carry the 3" is on the edge for length. For me the 3" barrel is right at the top of my Right back pocket with a holster with no extra length. On the Plus side for the 3" is a Full Length Ejector Rod and more sight radius. Either barrel length will work. Note: The 65 Snub comes in both Round and Square Butt. Round butt will be easier to find a compact grip for in rubber. Kim Ahrends make a Square Butt Boot Grip if you happen to end up with a Square Butt.
You will need to study on grips a litttle. A 357 kicks hard so rubber can help tame it down a little. The down side for rubber grips is being more grippy on your cover garment. Wood slides over your shirt much better.
Again I would carry in a Lobo Enhanced Pancake at 4 O'Clock.
I belt carry reloads in Safariland Comp II Speed Loaders carried in a CD-2 Spring Steel Carrier.
The Speed Loader Store has Free Shipping over $25 something to consider on the total price of your order. I find them a little cheaper when making a small order.
Myself I carry a S&W 442 Pro Moon Clip for my small light weight revolver.
My most carried K Frame would be my 3" Model 66.
I also have a 2" Model 15 Barbecue Gun.
I also carry my 2-1/2" Barrel S&W Model 315 Night Guard some.
I had a 2-1/2" Model 66 I traded for the 2" 15. It was a great CCW revolver also.
You have lots of choices that will work.