I believe if I understand your question, the linking between your Google account happens automatically (as it should) when you log into your Google account on your handset, and your contacts all synchronize. However it sounds like some of the merging of duplicates, and what number is the "default" number get lost? For this I would definitely recommend the Gmail application online. All you need is to login from a computer and select "contacts". Then just go under "more actions" and do "find and merge duplicates" That should give you just one contact per person. This is your best option if you have lots of contacts, some are duplicates, or other information not entered or organized correctly. It can be quite time consuming and tedious to do editing from the handset. If this is not what you are asking, you may have to rephrase the question slightly.
When you say "sync the default number" that is rather ambiguous sentence. For example, I log into Gmail, click contacts, and then select one of my friends. There it shows me the numbers stored on my phone (in the Google cloud). If I were to change the numbers shown, that change would be reflected when I grabbed the handset next. Are you looking to make one number the default number for that person? And have it do so automatically?
Edit: After doing a little more research, it looks like this question was addressed here at the Google forums. The last comment in the list (by ratgurrl) mentions exactly this frustration. And despite what you do on the phone, when you resynchronize you lose the preference settings you put in the handset, and the 'DEFAULT' will revert to whichever contact number is at the top of the list on that contact in Gmail. So the REAL answer until Google addresses this: log into Gmail, and move the one you want as the "default" contact to the top of the list.