Upon playing the game and watching the anime, many questions were brought to my mind. We never are really given much history about Giovanni. How did he grow up? Does he have a family? How was he raised? We as the audience are first introduced to him as he currently is, the 40-something Boss and Gym Leader. Answers to these, and many other questions, would prove useful when trying to figure out why he is the way he is and why he is after what he is.
I cannot say that I feel Giovanni's primary goal is to have rare Pokemon or money. Though, these things are useful to his many goals, but they cannot be his sole motivation for his actions. It can be deducted, however, that when gathering rare and powerful Pokemon they could be sold at high prices to collectors for money. Other powerful Pokemon may be distributed among the members of Team Rocket to help them with their many schemes. And who in the Pokemon World would need weapons of destruction when you have magical creatures at your disposal? The Legendary Pokemon could attest to this and even though in the World of Pokemon it is an unspoken rule that Pokemon only battle other Pokemon, on occasion there are those who have broken and bent the rules. Giovanni being one of them when Mewtwo was able to harm Gary in episode 68.
Rare Pokemon and money seems to be one of his many different schemes. Giovanni is first met in the games in the Team Rocket Hideout, so conveniently located underneath the Saffron casino. Interestingly enough, the casino turned out to be run also by Giovanni. If you need money to run your operations, that might be the best place to get it. And with lots of money comes power. It is easy to manipulate people with money through their greed. Could all of his plans be done for riches? Surely it is not for fame. The Rocket Boss is surely infamous but he is usually unrecognisable to others as the Gym Leader, which we can assume is also a paid position. In the anime he also owns the Pokemon Theme Park which is another source of monetary income. So all these points come down to the question: Why does he need all this money?
As stated above, money can be used to manipulate people. Was Giovanni's main goal manipulation? With it, it could be quite possible that he would be able to keep the authorities at bay, he could use it to purchase anything he wanted as long as he had enough of it, and employ hundreds of loyal rocketeers. I believe that with this money he was planning even larger, even bigger schemes. Did he want the fame? Did he want to be well-known? Out of his gains he was able to create Mewtwo, a Pokemon that was able to defeat all others. If he was able to do this as a Gym Leader, what would he gain? I think that he was simply testing out his "toy" for a bigger plan.
"My opponent is the leader of the most evil Pokemon Organization in the world! I can't let my guard down for a second!"
- Red; Pokemon Adventures Vol. 3, ch. 37
Do I dare say World Domination? I think it quite possible. Let us put aside the fact that Giovanni is quite possibly the archetype of the Archenemy and the criminal genius. His exploits are never clearly defined in the games or anime, simply that he is causing trouble for various reasons, mainly for money and Pokemon. He has all the given power at his disposal: hundreds of loyal followers, able to control authorities, able to mysteriously disappear, and having the most powerful creatures that could destroy lands in the blink of an eye. It could have been easily set up that he was planning for World Domination. I believe even some of the Rocket Grunts themselves believed that Giovanni would soon rule the world. His greatest plan, however, would never come to fruition. He would be thwarted at every turn and soon have to face his demise.