mdaniels,
Congratulations on your new LCR. You should be very happy with it! (I recommend the S&W 642 to new shooters because of its simplicity and quality. I consider the Ruger LCR to be another very fine choice and quite close to the 642.)
I agree with
The Bushmaster that you should probably try to get something as close to the feel of your LCR as possible. The S&W 317 or 43C should do nicely, but these are both quite expensive. A much cheaper option would be to look for a used H&R revolver in .22LR. These old revolvers are not built to anywhere near the quality level of your pretty new LCR, but they work fine and are usually quite inexpensive. You might check gunbroker or a similar sight. Also, Taurus seems to make several suitable revolvers. I very much like your recommendation from another post to actually "try-on" a gun to see which model fits you the best!
I totally agree with the advice to get a .22 for practice. The day that I bought my first gun (a S&W 642) I went to the range with a friend and between us we burned through $100 worth of ammo in just a few of hours. I immediately realized that it would be a very good idea to get a .22 pistol to practice with! (about $0.04 per round for .22LR vs $.35 per round for .38 Special... nearly 9 times cheaper!) I bought a Walther P22 for around $300, new. This little pistol is a LOT of fun, but it is not accurate at all, and it is a semi, not a revolver like you should get. (I did not know enough back then to try to match the platform... live and learn.)
Based on your other posts, you seem knowledgeable about bigger guns.
I don't want to insult your intelligence, but be sure that what you are getting is chambered in .22 LR and NOT .22 WMR! The Long-Rifle rounds are much cheaper than the Magnums.
Good luck, and welcome to The High Road!