We tend to use a mix of both European and Chinese manufacturers for our PCBs, with the decision usually depending on whether we need the board quickly (which usually means a European manufacturer like PCBPool) or inexpensively (most often PCBCart or perhaps Gold Phoenix). For single board prototypes, the prices all tend to be in the same ballpark (when you keep in mind shipping costs and delays, taxes and duty, etc.). If you want to produce more than 10 boards, though, the Chinese manufacturers start to be very competitive in terms of pricing, and at 100+ boards there's really no contest financially.
PCBPool already offers a DRU file for Eagle which you can download here (look for "Eagle DRU File"), but to make it easier to detect any potential problems when sending Gerbers off to PCBCart, we've made a design rules file for their "Standard PCB" service, which has the following technical limitations:
- 0.2mm (8mil) traces/spacing
- 0.3mm (12mil) annular rings* (see note on this below)
- 0.4mm (16mil) minimum drill size
PCBCart is able to produce boards with much tighter technical specifications than this, but you pay a premium for that so we usually stick to the standard settings unless there's a pressing reason not to.
To use the DRU file, simply download it and save it to the DRU folder where Eagle is installed. Once you have finished your board layout (or want to test the work you've done so far), you can click on the DRC icon 
, load the appropriate DRU file, and run the tests. If any errors are detected, Eagle will inform you of them and you can double-click on the warning to zoom into exactly where the problem is on your board. You should always make sure that your board passes the DRC check before sending it out for manufacturing.
PCBCart "Standard Service" Design Rules Check (DRU) for Eagle
| Version | Release Notes |
 | 0.1 | Initial Release (Beta) |
Someone with experience with PCBPool told me that they will accept up to 10mil (0.25mm) annular rings for their Standard Service, and we recently tried it ourselves. We didn't get any complaints from quality control, and have adjusted the DRU file accordingly for 10mil annular rings. If you want to be more conservative, though, you can set them back to 12mil in the 'Restring' tab.