Most modern games are not built from scratch but use some pre-existing game/graphics engine.
Flash games are quite popular. Although most games written in Flash tend to be simple, the language is geared towards graphics and you will really learn at the higher level.
C++ is really widely used, but it is unlikely that building a game engine from scratch is a viable idea.
Look at www.GarageGames.com for a good place to find both a ready game engine and a community of developers writing games.
