Using the MySQL libraries will GPL your code base.
If you're writing the code for multiple customers, you will be obligated to release the source code to you system to THOSE customers. You have no obligation under the GPL to open the source code to the public at large, you simply can not prevent someone else from doing so.
Let me repeat that, as people get really unclear about this point. The GPL obligates you as the entity distributing the software to release the source code only to those entities you have actually released a binary of the software to. If you have a relationship with me, and I get a copy of your software (and ideally I have compensated you for it), and then Frank shows up asking for the software, you have NO obligation to give (or sell, or anything) the software to Frank. It's not some "Cat out of the bag" thing.
Frank could come to me, and I can give (sell, trade) it to him, and you can not stop me from doing so, but you have no commitment to distribute the software yourself, nor support Frank. Since I may well be in the Tire business, distributing software really isn't my bag, so it's unlikely that I'll be posting code up on some public archive.
If the project is for a single customer, they may well be entitled to the source code anyway, so the GPL in this case is probably a non-issue.
As long as you have copyright to the code, you can always change the license for a future release. So, if you choose to no longer use MySQL later, you can "un-GPL" the next release and use some other license, however you can not "un-GPL" any released software.
For custom, vertical software, the GPL is really a non-issue as most companies simply are not in the software distribution business, and as a vendor you're not obligated to actually support anyone but your actual customers, rather than anyone they might have given the source code too. The primary concern is over trade secrets etc.
Mass market software is a different issue, of course.