Choosing a prepaid SIM card provider is rather straight-foward in China. That's because there is only one choice which is compatible for phones outside of China and that is China Unicom. The easiest way to get the SIM card is to purchase it in the airport. Otherwise, you have to try your luck finding it in random shops since they don't seem to be commonly available in convenience stores. Reload vouchers can be purchased in convenience stores though.
Do remember to clarify that bundled data for internet usage is included during the purchase though. One point to note is that the subscription plan (for bundled calls/SMS/data) is pro-rated, i.e. if you start on the 14th of the month, you pay for a fraction of the subscription fee from 14th to end of the month. That also means your bundled calls/SMS/data is also pro-rated. So, you do have to track your data usage very closely so as not to exceed the bundled data allowance. Also note that the self-help instructions via SMS are mostly in Chinese only, but it shouldn't be hard to access the common instructions by following my guide below. The last point to note is that reload vouchers are strictly for use if the prepaid SIM card is purchased from the same state, i.e. you cannot use a reload voucher bought in Guangdong if the prepaid SIM card is purchased in Zhejiang.
After your prepaid SIM is loaded into your phone, you will receive several welcome messages like the ones shown in the screenshot below. One of the messages will also show your phone number.
If you want to access the self-help menu, simply text "10010" to 10010 and you will receive the following message.
If you wish to check your available data allowance and your credit balance, simply send/reply 101 or 102 to 10010. Although the 2 menu items are supposed to be different, it seems that I get very similar SMS responses for both of them. Below is an example of the SMS response.
Related Guide: http://prepaidwithdata.wikia.com/wiki/China