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First off choose one, directx is faster on windows (microsoft barely supports opengl at all, because they want everyone to use dx, and I pretty much agree dx is better) but opengl is cross platform. Really though, not many non-windows users play games, and those that do know how to handle wine or dual boot windows to play games, and almost all linux users dont believe in paying for software.
I would go with dx, but thats personal preference. People say that opengl is easier, but that's not really true, it just provides utility functions that are only useful for people first starting and are too slow for actual games.
You probably should learn something other than delphi too, there is very little support out there for writing games with delphi.
go to amazon or a library if you want a book, go to gamedev.net if you want community support.