I guess California allows lever guns, but they may consider it a "cowboy assault rifle" and not let you have one....
I have a Henry and like it, though some will say to get a Marlin or maybe a Ruger 1022 instead. Any particular reason for the Henry? You like leverguns? The action is quite smooth and it's a very accurate rifle when you learn to shoot.
I've shot Federal, Winchester and CCI through mine and it has no problems with either.
The Henry comes with a handbook and it gives cleaning instructions. Buy yourself a standard cleaning kit and a boresnake. I've found the Henry doesn't need to be cleaned a lot each time you go out, but do it anyway. The boresnake seems to be a better fit than the regular rod, brush and jig set up. You'll need to buy the thin patches, the thicker t-shirt like patch material is too hard to get into the barrel and the force may bend the rod, use the smaller, paper thin patches like the ones made by Outers. You can find them at WalMart.
Gun safety is gun safety, doesn't matter whether you're talking pistols or rifles. Just follow the four rules and you'll be okay. Find a place that offers beginning rifle training in your area to help you get started. And don't forget to have fun shooting.