The StG44 is a really big, heavy .22. If you are not really into the history of it, I'd say it's not a very practical rifle. The sights are early-20th Century correct, and not very good. The mags are extremely long, making bench use difficult. The "cool factor" is off the charts.
The MP5, in any caliber, leaves me cold, but the rimfire version is going to be lighter, more compact, and with better sights, so probably more useful.
A shooting buddy has a rimfire SIG, which is some sort of "trainer" for the .223 version, and he really likes it. You might consider that.
Check out this video at about the 9:30 point, for some short reviews of the StG and SIG: