I have a boatload of .22 rifles. The only levers are two Winchester 9422's that I bought before they were discontinued and got stupid expensive. They are great rifles, but I wouldn't buy one at today's prices. I would probably go for a Marlin 39 instead.
I have no personal experience with the Henry, but I've seen a few at the range. People seem to like theirs.
If you want a semi-auto, the Marlin 60 is a great deal for the money. If you want a tinkering/project rifle, go for a Ruger 10/22 because of all the aftermarket goodies you can get. Otherwise, you'll get just as good a rifle for less money with the Marlin.
Savage and Marlin both make great bolt rifles for reasonable prices. If you want to spend a little more cash and move up one notch in "class," go for a CZ: either the old model 452 (my preference) or the new 455 that lets you swap barrels to let you use .22WMR or .17 if you want.
And then there's pumps. Older Remington 572 would be my choice (I have one), but the Henry pumps are popular too.