Hey Liz,
From experience I can tell you any transacting online in China can be a pain. First thing you should know is that unfortunately many merchants based outside of the mainland do not accept Union Pay. You’ll even find this to be the case in Hong Kong.
If you plan to be here for a while it’s worth setting up an Alipay account. It links to your bank account (via online banking), and opens up more possibilities for online purchase in China. I’ve used it for goods, flights, hotels and more.
Another issue is that some online banking services only work within an IE browser, so that can turn out to be a real pain. I personally operate three bank accounts in order to be able to cover all the bases. Again Alipay helps you get around this if you can recharge an amount in advance to it, and then you can carry out purchases on both Windows and Mac.
Another option/addition you could consider is a PayPal World account. You can attach your Union Pay account to the PayPal account and transact ‘cross border’ payments with any merchants who accept Union Pay.
Visa is not something banks generally offer as a ‘debit’ card option in China, and the criteria for obtaining a credit card is high. I believe Standard Chartered plan to introduce a Visa debit card this year, but that’s of no use right now. One final option is to find a way to obtain a ‘pre-paid’ Visa card from Hong Kong, which can be used with anyone accepting Visa, online or otherwise.