How Money (or the Lack of It) Affects Team Rocket
Team Rocket, both as a duo and as a trio, have been marked and wounded by money (or the lack of it) in their formative years. Three wounded individuals, traveling together, trying to make the best of things and often failing...which is an interesting, almost admirable dynamic, considering that they are the villains of the show.
Their Monetary Backgrounds

The Team Rocket duo is a study of opposites when it comes to money; Jessie grew up impoverished in an orphanage, while James grew up wealthy and raised by both biological parents. But that's not quite the whole story, especially for James--being wealthy did not make James' life any easier, since to maintain that wealth he had to give up all autonomy and doom himself to a life of being emotionally abused and controlled by bullying parents. Add Meowth's story of coming up trying to fight free of poverty, running with a Meowth street gang, and learning to talk and walk like a human for the sake of unrequited love, and you have three tragic tales!
Jessie and Meowth vs. James

Likely because of their beginnings in privation, Jessie and Meowth are both highly ambitious individuals, often chasing monetary gain to the exclusion of anything else. (Scarlett O'Hara's quote from Gone With the Wind comes to mind: "As God is my witness, as God is my witness they're not going to lick me. I'm going to live through this and when it's all over, I'll never be hungry again...If I have to lie, steal, cheat or kill. As God is my witness, I'll never be hungry again.")
This apparent philosophy can make both Jessie and Meowth appear selfish and even cruel--as long as they have enough for them, who cares about anyone else? Both of them are also more likely to throw each other under the proverbial bus if it means a gain for themselves. Their early experiences with poverty have made them desperate, but yet out of that desperation has grown a fierce drive to succeed, too.
The real outlier in Team Rocket is James. Having grown up in opulence and luxury, he started out arrogantly dismissing his own wealth simply because he didn't want to do what he was told. But after living on his own, and especially after serving with Jessie in Team Rocket, he displays a compassion that could make one almost believe he's a hero in villain's clothes.
The reason for this change? He has experienced both wealth and poverty now, a condition which Jessie and Meowth have never been through--and it changes him for the better. If he had not left his family and experienced hunger and failure, he could have remained uncaring about others. This knowledge affects Jessie and Meowth, who see James' example and seem to learn from it as they journey together as a team.
Success and Money = Happy/Good Team Rocket?

Because of their ineptitude at stealing Pokémon, Jessie and James are often hanging on to their last dimes and barely making do. But during the episode "The Fourth Round Rumble" at the end of the Indigo League season, we see Team Rocket making a decent living selling items outside the arena (even if their wares are basically just snacks and fake Pokémon badges drummed up by Meowth). In this episode, they both mull over the decision to become honest workers, and even have an idea for a restaurant they could own together. The craziest thing? They are not only excited about the planning, but happy in a way we've never seen them before, creating a very different version of their motto:
Jessie: That's not a bad idea. We can call it "Jessie's!"
James: "James'!"
Jessie: Want a burger and fries without trouble?
James: If you're really hungry, make it double!
Jessie: To protect the world from hunger and thirst!
James: Our food isn't bad, at least not the worst.
Jessie: The Team Rocket Restaurant; blast in for a bite.
Jessie and James: We stay open all day, we stay open all night!
(Meowth is appalled by this apparent change of heart, and vows not to let them "go straight" if he can help it.)
I think this at least hints that Jessie and James do WANT to be good and do WANT to be truly, genuinely helpful and needed, but they can only feel that way when their basic need for enough money to live on is met. It's a function of Maslow's hierarchy of needs; once Jessie and James feel more secure about their situation and feel like they have an actual place to serve in the "honest" world rather than the criminal world, they start to act downright nice! What an interesting development (and a telling one, given how most societies treat criminals these days).