I think metro style UI is just beautiful and user friendly. It is suitable for both Tablet and PC. Should I make my new website design in metro style or conventional standard?
It depends on what aspects of Metro you're talking about. If you want to emulate what they've been calling their "authentically digital" aesthetic of clean lines and squares, go for it.
There would be two thigns I'd warn against using though.
The hidden charms. In Metro/Windows8 you slide in from the top, bottom, and sides to reveal core functionality like switching pages, revealing tools, apps, etc. As an OS, you can expect that your users will figure this kind of thing out, but I feel that would be too great an expectation for a website that could be visited by anyone on any device.
The horizontal scrolling. Horizontal scrolling feels natural and efficient on touch devices, but is a big pain for people using Keyboard and Mouse.