This is (as you know) a massively involved question. It depends enormously on the nature of the product... Volumes? BOM cost? Level of Tech? The CM you'd use to make 10,000,000 greeting card modules on paper one-layer boards is very different than you'd want to make 1,000 pieces of a 19" x 19" 20-layer HDI PCB with $20,000 worth of parts on it. In between is an entire spectrum of possibilities. China is also so entirely about relationships that you REALLY need to have an introduction and preferably some prior contact with anyone you want to work with. You should also plan to have boots on the ground there often or even continuously, especially early in the process. Ideally that representative is someone Chinese who speaks the language and knows the culture, and has relevant relationships already in place. Although you then also need to be careful that those pre-existing relationships don't mean that "your" guy is more loyal to your vendor than to you. A good place to start that I just heard about last week from a co-worker of mine, and which sounds interesting is Dragon Innovation. I should emphasize that I have not used them myself, but I've heard good things about them...
Another question I would ask is "Are they sure that they want / need to manufacture in China?" The benefits of building there are shrinking, especially at the lower end of the volume scale. I have found more and more CMs in the U.S. that are willing to take on medium volume manufacturing at lower cost if you can give them lead time. They use those jobs to fill in gaps in their "primary" quick-turn prototype assembly. One place here in the Seattle area that I use for protos but which also does smaller end production work is Out of the Box Manufacturing. I use them to assemble boards, but they can also do full final product assembly and test. You can also "split the difference," and do the more commodity aspects of your manufacturing (e.g. bare PCB fab, or PCB fab + assembly, or shooting plastics) overseas, and then do final assembly, calibration, and test here in the U.S. You can also look into working with U.S. firms that have subsidiaries or partners in Mexico or elsewhere in Latin America.
A local design-and-project management firm that we use for a lot of stuff, and with whom I've had good luck, is Monsoon Solutions. They have relationships with fab houses and assembly houses in the US as well as internationally, and can help you find the right balance of cost, speed, and international entanglement. They will also maintain inventories of part kits and help actually design products as well, if you want. Of course, you pay for their expertise, but I've found it to be valuable. Obviously I've got a current bias for Seattle sources. Many of my Bay Area leads for this stuff are somewhat stale, since over the last few years my employers have either had direct relations with industry-specific ODM firms in China (hence my frequent travel!) or didn't manufacture in China at all... There's also a fairly recent profusion of manufacturing consultants on all this stuff, arguably making it much easier to get started in HW production.
Anyway, this only touches on some of the myriad issues. It doesn't even mention issues of Chinese vs. U.S. law , intellectual property protection, supply chain integrity, international shipping, and so on. As usual, the correct answer is "get expert help with this, because it's a monumental undertaking, and it's worth getting right." Good Luck!
