1) If one of the matrix is positive definite, you might want to use SSYGST/DSYGST/CHEGST/ZHEGST.
2) If you only want a few of the eigenvalues, then you do not want to use LAPACK. LAPACK uses direct method. So all cost will be O(n^3).
You want to use iterative methods where the cost will be closer from O(n^2) for a few eigenvalues. There are good packages out there.
The standard reference is ARPACK from Lehoucq, Maschhoff, Sorensen and Yang: http://www.caam.rice.edu/software/ARPACK/
It is used by matlab eigs function for example. This starts to be a little outdated and more modern alternatives would be:
PRIMME from Stathopoulos: http://www.cs.wm.edu/~andreas/software/
LOBPCG from Knyazev: http://code.google.com/p/blopex/
JDCG and JADAMILU from Notay: http://homepages.ulb.ac.be/~ynotay/
I think all three can solve symmetric generalized eigenvalue problem but one of the matrices need to be positive definite.