As ... as possible
できるだけ~
なるべく is also OK (either in conversation or writing).
I think なるべく is much weaker compared with できるだけ which is asking for effort or something to the full extent when used in request.
なるべく is more like "is possible".
なるたけ is similar to なるべく, though less commonly used.
I've never heard of なるだけ.
e.g.
できるだけ早く来てください。 Please come as early as possible.
なるべく早く来てください。 Please come early if possible (I'd be grateful if you could come early.)