For 38/357 the favorites are probably a S&W L-frame or a Ruger GP-100. My personal favorite of many is my single-action Ruger Blackhawk.
There are quite a few entry-level 1911's available in the $350-$400 range which function just fine. Personally I would be willing to pay a little more for larger sights than the basic GI model comes with. Other than that, the basic model is all I need. Rock Island Armory is probably the most common inexpensive 1911. My FiL got an awesome Metro Arms model with nice sights and a few other "extras" for $360, but that was super lucky.
In 44 magnum the most-recommended would probably be the S&W Model 29 (or whatever it's called these days) or the Ruger Redhawk. I personally prefer my single-action Ruger Super Blackhawk, but I REALLY like single-action revolvers.
I have a bunch of 380's. For CC an LCP or P3AT is extremely convenient. Just for shooting, the Beretta 84 is very nice. I prefer my CZ83 by a small margin. My very favorite is tbe Colt Government 380, pretty much a mini 1911. They were made in the 90's and have very low recoil due to steel construction and firing from a locked breech.
My favorite 40 is a 1911. My second favorite is my Beretta 96 - it is pretty much the US military pistol, but in 40 caliber. I very much prefer my 40's to be steel-framed, or at least alloy-framed.
Some of these pistols, such as the two Berettas and the CZ83, are readily available as police/military surplus. Those tend to be carried a lot and shot seldom. I got all three as surplus and paid something like $220, $300, and $330 for them. CDI Sales on Gunbroker is a great source for things like that.