Unless you are already at a high proficiency level (JLPT N2 or N1), I would recommend starting with a very basic level of the Kanji Kentei. While you are correct that vocabulary is an important part, if you do the test or practice tests, you will realize that you need to know kanji readings, radicals, meanings, stroke orders, antonyms, correctly producing written kanji, etc. In other words, you need an all-round solid knowledge of the kanji on that level of the test. I suggest using books which target specific levels, and by starting at Level 10 just to familiarize yourself with the test itself. Have a look at this series on Amazon Japan.
If you want to be very thorough, you could make your own vocabulary lists of common words. You could start by cross-referencing the Kanji Kentei kanji (see here) with frequency-based vocabulary lists, such as the ones here . By doing that, you can isolate the most common words associated with each kanji on the Kanji Kentei level you are preparing for.
This is a good link for cross-referncing kanji and vocab: