Again i am surprised that picking is not a more commonly available feature, if not the graphics library then something els.
It's not that it isn't "available". It's just that it's such a small and specific thing that it's not advertised as a "major feature" of any given game engine or toolkit. It's the same as car manufacturers not making a deal out of their cars featuring blinkers.
I would think that any half decent game engine allows you to select polygons by picking, so just select the one that you fine nice otherwise and then find out how to do the picking. It helps if the engine has a user community as then you can usually find tutorials or code snippets on the internet but, as I said the picking could be done completely separately, bypassing the graphics engine completely.
I have worked with a couple of in-house game engines that actually provide ray casting (which can be used for picking among other things) only against the physics objects, rather than the graphical objects. The physics objects are usually a lot simpler than their graphical counterparts, in terms of number of polygons and vertices, so they don't line up perfectly with what you see on the screen. This is another reason that I tend to think of picking as not being part of the graphics engine.
That said, if you really want to select visual polygons you can do it with the technique I described above. If you are unsure about the math just ask, or do a google search using the steps I provided as search terms. Also, depending on how complex your scene is, you might be able to skip the AABB test completely as it is just an optimization and go straight from the ray construction to ray-triangle intersection, iterating over all triangles in the scene.