The two countries that are obviously easiest for you to both live and work in are either England or China. In China she does not need a visa or work permit, but you do. In England you don't need a visa or work permit, but she does.
In any other country, you both need a visa and work permit.
If you were married, it would be easier. Countries usually have a visa that can allow spouses of citizens of that country to stay with their spouse. There are usually financial requirements, but once you have the visa you still need to get a work permit. Similarly, if you were in any other country than England or China and one of you were able to get a work permit, there are usually ways to get a visa as a dependent. Not being married means this is not available.
Getting a work permit can be difficult, depending on the country. But if you have (or she has) skills/qualifications in a good field (e.g. technology or similar) it's not too difficult. In many countries a degree is required (or at least strongly recommended).
Unless you are from Northern Ireland or she is from Hong Kong or Macau, neither of you qualifies for the US green card lottery, which is the usual other suggestion.