The Browning is a fine gun, but it feels like a child's toy to me. And the trigger isn't great.
I have a couple Marlins, one with a 20" tapered octagon barrel, one with a 24" heavy round barrel. I like them both, and so does anyone else who shoots one. I never planned to buy two; I just really liked one of them and the other one, a rare 35-year-old version I really liked, showed up at the store, so I broke the piggy bank and bought it. The 24" is a great practice gun for a 336 or other larger lever action. My only complaint is that the lever can beat up the tops of your fingers, since it's impossible to just shoot a few rounds with it -- the 24" has a 19-round magazine (more if you shoot Longs or Shorts) and it's just so much fun you just keep shooting. Before you know it, you've shot a brick and your fingers are sore on top.
I finally made a fringed 2-layer suede lever wrap for it yesterday evening; I'll be testing it out with live ammo tonight or tomorrow. Preliminary tests are really positive.
I like the Henry octagon; I might have bought one of those if I didn't find the old Marlin with the octagon barrel. I have reservations about the Henry's stock drop, but it's a neat gun, US-made and not too expensive. The Marlin, though, has a steel receiver and is a takedown. You do get more when you pay more; the question is, "Does it matter to you?" Also, you can't buy a new Marlin with a 20" barrel and a straight grip, and the used ones are not cheap. NIB, Henry is probably your best option. OTOH used 39M's will hold their value if you don't trash them.
All three rifles are well-made and have their adherents. I think you can probably get a bit more accuracy from the 24" heavy barrel Marlin, and it has "real-gun" heft. Feels about like a 336. If it's for a kid, get the Henry youth model, which is smaller, lighter, and cheaper, and will work great. If it's for a grownup, though, the Marlin is a grownup gun.