Can one prepare and bathe for the mikva at home and then go to mikva and immerse without bathing or showering at all at the Mikva? I heard that one should be wet before going into the Mikva. Is that true?
There is no requirement to be wet upon entering the MIkvah.
If the entire bathing process is not being done in the mikvah, common custom is to take another [quick] shower and comb out the hair before the tevila. This is because there is generally some time span between the bath and tevila, even an hour or so. If however, a woman bathes/showers and immediately goes straight to the mikvah, there would be no requirement to shower again [some prefer to do so anyway,which is fine], even if she is dry.
Keep in mind that this is with regards to chafifa/bathing/cleaning. In any event immediately before tevila a woman must carefully and methodically check over her whole body, not in a rushed manner. This is crucial from both a halachic and practical standpoint.