What is out there and what would you recommend?
Current production rimfire leverguns out there are the Henry, Marlin, Browning, Mossberg and Uberti. The Henry outsells the others by leaps and bounds. This is due to relatively low cost, outstanding customer service, made in America, and the fact that their guns are the smoothest shooting rifles of the bunch, past or present. The most popular rifles are the Henry, Marlin 39 and the Winchester 9422, with the Browning BL-22 well behind the others. The Winchester (discontinued) and Marlin are very fine rifles made from forged steel and walnut, and both are collectible. They are also the only two takedown rifles of the bunch. The Browning is a beautiful little Japanese made rifle that uses a combination of steel and alloy, along with some very nice walnut on many examples. The Browning uses a unique, non-traditional lever/trigger assembly that moves together and results in a very short, quick lever stroke. I've only handled the Mossberg and wasn't impressed, due mainly to the two external safeties, the rebounding hammer, the so-called hardwood, and the price.
My recommendation? Henry if you want a smooth, easy shooter and are are on a budget. Winchester or Marlin if you want an exceptional rifle that would make a great heirloom. The browning if you want excellent fit/finish with heirloom quality and won't be bothered by the non-traditional lever design.
One more thing...if you go for the Marlin then do yourself a favor and look for an older one (pre-Remington) in nice condition because the new ones seem to be plagued with problems.
Best of luck in your search!