「なるベく」 should be considered a single word meaning you want to do something or want something done "as [...] as possible". For example, 「お問い合わせはなるべく短めにお願いします。」 would mean "Please keep any inquiries as short as possible.".
The 「～べき」 suffix gets attached to verbs and means "should", so 「なるべき」 means "should become". For example,「なるべきようになった。」 means "It is as it should be."
So basically,「なるベく」 is used when expressing intent (when the subject is the 1st person) or making a request (when the subject is not the 1st person), whereas 「なるべき」 is used intransitively as a qualification of how things are or are supposed to be.