The Marlin Model 39 gets my vote. Dating back to the end of the 19th century, one of the oldest (if not the oldest) continually made rifles made in America (if not the world). Steeped in history and made entirely from forged, machined steel parts and American black walnut, it's the .22 lever-action rifle all are (or should be) compared to.
I have had the pleasure of shooting two of the henry lever actions, the h001 and the model with the octagon barrel. I enjoyed them both and they were both accurate and extremely fun.
If you want a well made classic rifle you'll be proud to hand down to the grandkids look for a used Marlin 39 variant or a Winchester 94-22. No personal experience, but the Browning gets good reports too. I like the Winchester a little better.
If you want an inexpensive, well made gun the Henry is hard to beat. It is the 10-22 of lever action 22's. It will never be a classic, but should give years of good service.
In my case the Browning lacked the expected accuracy, but the Henry was fine. I really did like the Browning, it's a sweet little honey to handle. I'm sorry it didn't give me what I wanted shooting aspirin tablets at 25 yards. Absolutely it had plenty accuracy for small game hunters and plinkers. Just could not reliably hit cheerios & peanuts at the local "fun shoots".
I am very pleased with my Henry and the warranty speaks for itself. The Henry warranty is simply:
Henry Repeating Arms stands behind its products as it has historically. We offer a simple limited lifetime warranty; if you have a problem at any time, and it's our fault, we will correct the problem immediately and at no charge. The warranty does not cover excessive wear and tear to parts, and accidental damage.
I love my Browning BL-22. Beautiful, accurate, and the short-travel lever really sets it apart from the competition IMO. Nothing wrong with the Henry or Marlin either. Mossberg makes a pretty nice .22 levergun too, the 464-.22. It's a pretty close copy of the old 9422 Winchester.