My question is, should i use wifi.h library ?
Use it for what? If you want to talk to the WiFi shield, you need some kind of library. The one that goes with your hardware is always best.
and always what i am getting in my serial is - "Attempting to connect to SSID".
Then, why are you worried about what needs to happen after you successfully connect to the wireless router? Connecting to the wireless router is essential if you are going to do anything with the network.