I planning to buy an Android phone of medium budget so I need your help to find out the best so it does not hangs and works smoothly, it should support most apps in the play store?

Samsung galaxy SIII Mini
Samsung galaxy grand
HTC One SV
HTC Desire X

All of recent phones with Android 4.1 or above works smooth unlike it was with 2.3.3 or below. The chepest are always Nexus branded phones as it is Google idea to get developers good spec devices with latest OS available. You can buy Nexus 4 either from Play Google (SIM free, not locked with network) or buy it with your local mobile provider.