The main dictionary I used to help with definitions of Japanese words
was Jim Breen's EDICT (http://www.csse.monash.edu.au/~jwb/japanese.html) I also recommend
the Japanese dictionary JDic (web version is here: http://www.csse.monash.edu.au/~jwb/wwwjdic.html which uses his EDICT files. If you download Glenn Rosenthal's JWPce Japanese word processor (http://www.physics.ucla.edu/~grosenth/jwpce.html) you can also get a handy version of the EDICT dictionary that will run locally on your computer (and even a PDA/smartphone).
The basic kanji required for fluency in Japanese are the Joyo kanji and are widely known. The order that the kanji appear in Pera-Pera Japanese is based on the order in the Kumon (http://www.kumon.com/) teaching system used to teach Japanese children as well as foreigners. Note that outside of Japan most Kumon centres teach maths and some native reading, not Japanese.
The vocabulary files are available widely at a number of sites including kanji-a-day.com and are based on the the required vocabulary lists for the JLPT test, released by The Japan Foundation, who run the test. These files were combined into a list by Thierry Bézecourt (Copyright © 2001 Thierry Bézecourt (http://www.thbz.org)) with English translations by Norbert Burger. I f you want to expose yourself to more kanji and test what you have learned using Pera-Pera Japanese, kanji-a-day.com is well worth a visit.
I was inspired to make this site after seeing the book: "Remembering The Kanji" by James W. Heisig.
Hopefully, by learning Japanese you have come to appreciate the beauty of kanji. Now you can wear them too! At http://www.printmojo.com/kanjiTs/ you can purchase T-shirts with kanji designs drawn by a talented Japanese artist.