If you want a used gun with a beefy frame that will fall within your budget, consider investigating the famous S&W Model 28 "Highway Patrolman". N frame, most commonly found with a 4" barrel. The bluing varies. I've got two and one is almost a polished look and the other is pretty much a matte black. Both are the 28-2 models. They have adjustable sights and are very accurate. These are the workingman's Model 27.
https://en.wikipedia.org/wiki/Smith_%26_Wesson_Model_28
You can thank me after you get one.