You want your shutter speed to be at least as fast as your focal length. In other words...
28mm - at least 1/28sec
50mm - at least 1/50sec
200mm - at least 1/200sec
When using Aperture mode the shutter speed is set to meter correctly for a given ISO. If you have a fixed ISO, say ISO 100, then the camera will likely set the speed slower than what you want unless you are in bright light, particularly if aperture is set for more depth of field. However, setting the ISO too high, while it will almost always get you a good shutter speed, will likely give you more noise in your photo than you want.
Given your level of experience I would say your best bet right now is to turn on the Auto ISO function on your camera, and set the max ISO to, say, 1600 (depending on the camera it could go higher) and the current ISO to 100. This way, the camera will choose an ISO setting that will allow the shutter speed for a given aperture to match that of the focal length (if you have a 50mm it will shoot at 1/60sec or faster) by raising the ISO to the minimum level that will allow for that. This could give you more noise in your photo than you might want, but better to have a crisp photo with noise than a blurred one without it.