Singapore is probably the best place to start your first trip to Asia. It will be familiar enough but with some Asian touches. After that you can move on to the “real Asia”...

And don’t forget Hong Kong. It was for me the first city visited in Asia, and it absolutely blew me away. (I would even suggest limiting China to Hong Kong only on your first trip unless you have plenty of time. No visa needed, which makes it easier to organise...)