I'm going to assume that when you say you're new to Japanese, you mean you've been studying it for less than two years. I think of myself as an intermediate student at six years of study, and I'm probably flattering myself.
Although there are a number of books designed to teach the Kanji in a systematic or mnemonic fashion ("Learning the Kanji," "Kanji ABC"), personally I found simple flash cards to be most useful for my Kanji studies. I started with a Kanji book much like the one you describe and used this to write my own 3"x5" cards. Although commercial Kanji flash cards are available, I feel that the act of writing the cards also helps in memorizing them (if only a little). My book grouped the Kanji according to which characters were taught in each grade of school, and I memorized the cards according to these groups.
The way you go about memorizing the cards could be very important. Working with each "grade" (about 200 characters) at a time, I would first memorize them in order (I numbered my cards for this purpose), and then after I felt I knew them well, I would shuffle them and start memorizing again. Shuffling is of course vital, otherwise you'll only learn them in order. I would spend about 3-6 months in memorizing each group, and woud of course review previous groups every week.
I found that the best time for studying my cards was in the evening while I relaxed or watched tv. Even though focusing on the cards helped me memorize them faster, glancing at them while I was distracted was still useful. However, the nice thing about flash cards was that I could study them anywhere and at any time. (I've heard that students in Japan will make small flash cards for English and put them on a ring so that they can easily carry them wherever they go.)
If your memorization process is anything like mine, you may find that when you add a new group of Kanji to memorize, the characters that you already know may now seem indistinct for a while. This was alarming to me at first, but steady review of previously learned characters every week or so helped to firm up the old information again in a short while. I can't emphasize enough that constant review is important both for making progress and retaining what you have learned.
Please note that at first (and still, to an unfortunate degree) this was primarily a process of "recognition memorization" for me. Unlike Japanese school children, I only memorized the characters so that I could read them, rather than being able to write them. That may have been a less than optimal strategy. Perhaps one of the reasons new groups of characters seemed to interfere with old groups for me was that memorizing for recognition didn't encourage me to remember the details of each character. Many of the Kanji are very similar to each other, with only a single stroke to differentiate them. When you learn to write the characters, you necessarily learn actual stroke-by-stroke recall of them, rather than just recognition. (How difficult is recall versus recognition? Well, is it vastly more difficult for most people to draw a friend's face from memory rather than simply recognizing a friend's face.)
Of course, "stroke-by-stroke" recall is not always necessary. Most Kanji characters are made up of groups of simpler characters. Once you become familiar with these groups, you can simply remember them as chunks, and remember more complex characters as combinations of these chunks. Books like "Kanji ABC" take you down this route, teaching you the simple characters first and them combining them as you go along. Although I feel as though this approach tends to give you a less detailed knowledge of Kanji in the long run, I find that knowing the meaning behind these simple characters (or "radicals") can help you greatly when you're trying to create your own mnemonics for complex characters.
(Here's a hint for remembering the onyomi of more complex characters: often characters share onyomi with their most complex radical on the right, or less often on top. For instance, 帳 has the onyomi "chou," the same as 長. However, please note that this is only a rule of thumb, not an actual rule. Similar characters may not have similar onyomi at all.)
Although you can expend countless reams of paper practicing your calligraphy, for the sake of the environment I would recommend computer programs for this purpose. One that comes to mind is "King Kanji," which you should find online easily. This application also comes in a version for handheld computers, which I consider even more useful (drawing on the screen of a handheld with a stylus is much more natural than using a mouse to draw on a PC screen).
Learning the Jouyou Kanji took me about four years, and I still don't feel as though I have mastered this character set. I review every day, and practice reading as much Japanese as I can. (Watch out for manga with furigana -- I feel as though these "cheat characters" actually erode my Kanji memory.) One good site that encourages daily review is
http://www.manythings.org/japanese/daily/, which presents 36 different characters each day.
I hope my suggestions are useful to you. Good luck!
