I've owned all four (Marlin 39A, Winchester 9422, Henry, and Browning BL-22). All four are very nice in their own ways.
The Marlin is the earliest design and utilizes forged steel for major components. The Winchester is the strongest and most refined. The Browning is the most compact and typically has the best finish. The Henry's origins are rooted in Germany and features the smoothest lever action of the bunch. While the Marlin 39's roots go back to the late 1800s (Model 1897), the other three were introduced in the 1970s.
My least favorite is the Browning, simply because I find it's short throw lever a bit stiff and awkward. The Henry is fun to shoot, but if you have an aversion to a painted alloy (Zamak) receiver, or a few plastic parts you'll want to look elsewhere. (The lower receiver of the Browning is also made of aluminum alloy). Fit and finish of the Marlin is generally the lowest, but it varies quite a bit and some examples are very well done. The Winchester is very nice in every way.
Accuracy is going to depend on the particular gun, but of the ones I've owned the Marlins were the most accurate. If you are going to shoot it alot, I'd stay away from the Marlin and Winchester since parts availability will likely become an issue with those discontinued models.
Whichever you choose, it will likely bring some enjoyable 22 plinking.