Where do I start… First, if you are going to travel around a few cities, you may want to get a tour company to arrange this. I have been to over a dozen cities in China, and fortunately all my trips have been arranged by locals, but we are thinking of using Odynovo Tours [www.chinaodysseytours.com] for a longer visit.
China has 20,000 km of high speed trains, and it is better to go by train than fly if you are going between cities that are relatively close. However, for a non-Chinese person it is very difficult to get tickets. Even if you book in advance, the office to collect the tickets can be hidden away somewhere, or will take an hour of queuing up. If you don’t book in advance, the queues are even longer and the seats may well be sold out. Negotiating all this could be a challenge for a first time visitor.
Best time of year is probably what they call the “golden spring” though make sure your visit doesn’t coincide with a big national holiday, especially those when people go back to their home towns.
As to learning some of the culture and history, the BBC had an excellent series that you may be able to buy or download.
Once you get there, it is pretty easy to get around and all the cities I have been to have adequate signage in English. In the bigger cities, especially Beijing, take the subways. Beijing’s traffic is horrendous, but the subways are very easy to use and to get around most of the things you would want to see. You can buy metro cards from vending machines that have an English option. Try to avoid peak hour. The trains are always crowded, but peak hour is even more challenging.
Most cities have subways to the airport (unlike e.g. Melbourne) and these are the quickest option to take. But if you fly to Shanghai, take the mag-lev train to Pudong, where you can either stay at one of the fabulous hotels (Shangri-La is one of the best I have stayed in) or get a subway to other parts of the city.
As to what to take - a camera, obviously. Maybe get VPN for your laptop (e.g. abc news is blocked in China). Most things you can get in Australia you can get in China. The only thing I noticed that is much more expensive is wine.
The people are usually very friendly and helpful, though outside the biggest cities, most above a certain age won’t know English. Learn a few phrases - people will appreciate you taking the effort.
Someone mentioned smoking. This is now banned in hotels and (I think) in any public enclosed space including malls and restaurants. It is not much worse than here.
China is a very exciting and vibrant country to visit. I hope you have a great time!