The Henry's are good shooting rifles and the least expensive of the bunch. Be sure and check out the sights on the standard rifle and one of the octagon models(Golden Boy or Frontier) because they are quite different. The octagons have much finer front sights along with a buckhorn rear sight.
My son and I were out shooting some lever .22's earlier this week. I was shooting a GB, and a Marlin 39A that was made in 1954. Accuracy-wise, there wasn't a bit of difference between the two. The sights were very similar and they were both hitting their mark anywhere between 25-60 yards. The only real difference is that the GB has a much smoother action which allowed me to stay on target easier between shots and to get quicker follow-up shots onto the target.
Personally, I've always been partial to the Winchester 9422. Construction-wise, the 9422 and 39A are king, but I don't think either one has an advantage over the Henry when based soley on performance.