My dad has owned a marlin lever action forever, it was the gun I learned to shoot on 30 some years ago. Still functions great and looks pretty good too.
I used to own a henry .22 and would have no problem suggesting one to someone. Very nice action and probably the most accurate out of the box .22 I have owned. I'm talking like 1 inch groups at 100 yards off from a bench with a high powered scope and the right load.
It is one of the few guns I wish I would not have sold.
I would say if you can afford it, get a marlin, if you are on a budget get the base model henry. Both are nice rifles.
My honest opinion though would be to shy away from the lever guns and get a good bolt action, like a savage with the new accutrigger. With a bolt gun you can pull the bolt and clean it from the back vrs doing it from the front where you could damage the crown and ruin your accuracy.
Lever guns are fun, just sort of a pain to clean. Not the best for bench shooting either

. They make real fine hunting guns though because they will feed anything you put in them.
I have no experience with the browning, but I would imagine they are nice enough gun. Haven't met a browning I didn't like.
Paul