I have seen too many people, on too many occasions confusing what GPL is about. Most common error is to think that one can not use a GPLed product with a commercial application. More sophisticated version of the confusion is some mumbling that involves the word "derivative" :-)
I think the root cause of the error is that 1) GPL License (as any legal document) is obscure 2) GPL FAQ that is intended to remove the obscurity is too long and it is hard to find the important piece within it. But there is a piece that clarifies many things, stating:
Question: I just found out that a company has a copy of a GPL\'ed program, and it costs money to get it. Aren\'t they violating the GPL by not making it available on the Internet? \
Answer: No. The GPL does not require anyone to use the Internet for distribution. It also does not require anyone in particular to redistribute the program. And (outside of one special case), even if someone does decide to redistribute the program sometimes, the GPL doesn\'t say he has to distribute a copy to you in particular, or any other person in particular.
What the GPL requires is that he must have the freedom to distribute a copy to you if he wishes to. Once the copyright holder does distribute a copy program to someone, that someone can then redistribute the program to you, or to anyone else, as he sees fit.
What does this mean? GPL does not prohibit you to use your software, of any license kind, with GPLed ones. Constraints only arise when you decide to ship your software to third parties (which, if you are developing a web application for own usage may never happen). GPL does not require you to publish your code that you use with a GPLed software, but it prevents you from denying others the right for redistribution once you give them your code.
Bottomline: GPL prohibits you from prohibiting others, does not require you to do anything in your own world.