I concur with Gerolf:
Get yourself legal advice if you want to be sure (or, perhaps, contact Digia sales department on this)
LGPL should fit, as it does not restrict the licence of the work derived from the library. That means you can choose a closed licence (as is most often done), but it should also mean that you can choose a very liberal licence like you plan to do.
It is my, non legal opinion that LGPL allows static linking as long as you provide some other means to satisfy the LGPL requirement that it must be possible for the user to replace the version of the library used (so, that means: relink the binairy).