The .357 Magnum is a very versatile cartridge. The revolvers were made in all four of the standard frame sizes. The fact you can shoot .38 Specials in them is another plus.
You mention the N-Frame as being too big for the .357. I disagree. Yes, it is pretty big, but not all that big. I bought an IWB N-Frame holster from LOBO and I carry a 4" M28-2 in total comfort.
If you just want a shooter the N-Frames are great. The M28 is the less expensive version of the M27, which has a better finish and checkering on the topstrap. Mechanically they are identical. They will probably outlast you.
The L-Frames are basically a stronger, slightly larger K-Frame, made to fire the .357 Magnum. The fixed sight ones are the M581 in blued and nickle and the M681 in stainless. Adjustable sight versions are the M586 and M686.
The K-Frames are no longer made in .357, but they are readily available used. The M13 and M65 are fixed sight guns and the M19 and M66 are adjustable. You should avoid a steady diet of 125 grain loads in the K-Frames, but 158 grain loads should keep it running for a long time.

There are a few I didn't mention,like the M520, a fixed sight N-Frame that was only produced for a short while and is very scarce. Also the J-Frames, but they are better for concealed carry.

Go ahead and try as many as you can. They are addictive.
Jim