How do you find high-quantity prices for ICs?
Generally be careful of just getting full BOM pricing from China.

I usually let them handle generic parts, resistors, capacitors, generic diodes, generic transistors.  That type of thing.  Production houses usually buy such parts in the 100k + lot size making them hard to beat.  When your prototypes come back for checking i strongly urge you to test the parts they used.  Its not uncommon for them to slip in 5% parts in place of 1% parts.  

If there are parts where the exact tolerance or dielectric is critical i would supply these yourself.

If you have a good relationship with the production house, you can let them source some of the IC's as well, common parts like op amps they can usually handle but again, test, test, test to make sure its not some relabeled piece of crap.

For the rest of the parts, i usually go with a major part supplier.  Arrow is my favorite so far.  They have a wide array of parts they stock, maintain warehouses and contacts in China to work directly with manufacturing and my local contact is very responsive and happy to dice up the order however I want.

What i normally do is get a full BOM price from both arrow and the manufacturer.  Then i sit down and cut up the BOMs based on who is giving the best prices.  Then i move anything that is on the China order that i'm concerned about the quality of over to arrow if the prices are reasonably close.

You may find that after a few runs you feel more confident and have a better relationship with your China manufacturer, at this point you may want to move more part sourcing to their end.  There absolutely are some trustworthy and capable production houses over there, there are also some very shady operations.

Another recommendation for dealing with Chinese manufacturing:  Be very, very methodical with your test procedures.  Use simple, direct language and lots of photos and diagrams.  Remember that the average test technician probably doesn't speak much English.   

Don't expect that they understand what the circuit does or be able to provide much debugging value.  They are very efficient at testing given a solid procedure but generally don't have the time to understand your circuit or put much thought into attempting debug solutions.