I think I am with Randy on this one. The model 37 is a very neat gun. You get the bottom ejection you like in a much more minimalist package than the Browning - particularly in the older guns. I personally am a really big fan of the Model 12 in 16, but a really nice one will run a bit more than $500, though a servicable one for not that much more. The old A5 "Sweet Sixteen" is one of the classic guns of the middle half of the 20th century. Great guns, though no A5 was ever accused of being light or particularly elegant. My only caution would be that the occasional Browning can be a little cranky. I think I would cruise the web and your local shops and grab either the Ithaca or the Winchester depending upon where I found the first best deal.
