I have an AM-3 and, although kinda cool, it is not the gentlemen's knife you are looking for. You would have to go out of your budget to get a proper Al Mar. Sure the AM-3 is cheap, but you get what you pay for and it is AO with no real easy way to open it unassisted (even with the thumb studs)...which probably disqualifies it from the gentlemen's knife category.
I also have several Leeks and I love those but same kinda deal...not really a gentlemen's knife. You can get a deep clip for the Leek if that is what you go with though.
The knives that come to mind when I think of gentlemen's knife range from old-timey traditionals to slipjoints to lock-backs but there are definitely more modern equivalents that most like these days. A lot of them are out of your price range but you can find a decent Kershaw or Kizer that would work just fine.
I've had a Kershaw Chill for many years and it was my primary EDC and backpacking knife until I could afford something more expensive. It is super light, unassisted, cheap, just the right size, not offensive to pull out and use in public, and it has a decent blade too. I highly recommend at least trying the Chill out. It is a flipper though but you can open it easily without an aggressive flip or thumb studs.