I actually applied for a Chinese visa today at the consulate in San Francisco, which is not in my home country (based on nationality) with no issues at all.
Single entry visas are normally valid for only 90 days from the date of issue, however at least in the US they will give you an extra 90 days (180 total) on request and with suitable documentation. This is probably your best option presuming you can show travel plans in the 90-180 day region.
Multiple Entry visas are valid for 6 months, however at least for US citizens they apparently do not normally issue a multi-entry visa until after you have been issued with and used a single-entry visa. From what I've read, this does vary from country to country.
You can obtain a visa outside of your country of citizenship, although again this may vary from consulate to consulate. For application in the US by non-US citizens you are required to show proof of legal status in the US (eg, US Visa, I-94, etc).
Note that China does require documentation of your travel plans before they will issue a Visa - that includes a confirmed flight ticket, and confirmed accommodation plans and/or an invitation letter from whoever you will be staying with.
Most Chinese consulates have fairly complete web pages with details of the requirements and details of visas, so I would suggest checking the websites for the consulate nearest you, and the consulate in the country(s) you expect to be in during your travel in Europe to confirm which option will be best. I also found the San Francisco embassy to be very responsive to questions sent to them via email (even replying on a Sunday to answer my question!)
An interesting side effect of applying in a different country - if I'd applied in my own country, the visa would have cost US$90. Applying in the US, it only cost $30. That's a nice little saving :)