I am a .22 rifle addict, and am particularly fond of lever action .22 rifles, I own a Henry H001 (the cheapest Henry), a Winchester 9422, a Browning BL22 and newer Marlin 39A.
Some thoughts on each:
If you want a Marlin 39A, get one of the older ones without the rebounding hammer. Mine (with rebounding hammer) took two trips back to the factory to cure it's failure to fire (light primer strikes) and failure to eject issues. Seems to be OK now, 500 rounds through it since it last came back from repair. It's a full size, heavy rifle, quite accurate. Marlin has now been aqcuired by Remington, and the New Haven Conncticut plant where the 39A was made is now closed, so getting even one of the newer, problematic rifles may be difficult. Much easier to get an older used one...
The Henry H001 is one of my favorite rifles, great value for the money. I paid $249 for mine brand new, it's smooth and accurate, and hasn't had a hiccup in the thousands of round I've put through it. I like the sights on the Henry better than any other of the lever .22's, it has a blade front sight and square notch rear, while the others have some sort of bead front sight. To me, a bead front sight obscures the target, making fine accuracy harder. With my first box of ammo through the rifle, I was hitting golf balls at 50 yards. It is light at 5.5 pounds, has more of a utilitarian look and feel to it, but it is a great rifle.
The Browning Bl22 is one of the higher grade, engraved rifles, got it used, 1994 or so vintage. It is the lightest of my .22 lever rifles at 5.0 pounds, prettier than a speckled pup, but has a horrible trigger, probably greater than 8 pounds. This hurts it's accuracy some. Has a short stock, so might be good for those with younger shooters in the house. The short lever throw does make it fun to shoot, but the accuracy limits it to a 25 yard rifle for me....
The Winchester 9422 I have is one of the first year 9422 "XTR", with the high gloss stock and metal. It is accurate and smooth, weighs about the same as the Henry at 5.5 pounds, great trigger. Owning and shooting it makes you feel like you own a Cadillac Eldorado, it is that nice. Bad news is they don't make them any more so you have to be prepared to pay some big money to own one (500-700 dollars). Worth every penny of it if you find a nice example.
So, if you want a field grade .22 lever rifle you don't mind letting the kids use or throw into your truck, get a Henry. If you want a legacy rifle, a desirable collectors piece, get a Winchester, older Marlin or Browning.