When the government doesn't give handouts, nobody can take something they're not entitled to. The farther 'left' you go, the bigger the handouts get, and the more people are compelled to cheat (the easier it gets, too). The benefit to society might outweigh the losses, but there's a lot of righteous indignation there. Freeloaders, huge welfare families...but that's probably not the way you want to go.
One big crux of a lot of arguments, once you drill down to it, is that socialism degrades people, corrupts them a bit, keeps them from living up to their true potential. You want to focus on the kid who might have aspired to be a mechanic or a factory worker--maybe he didn't have an amazing future, but he could have taken care of his family, been a good man--but instead, he found that it was easier to rely on welfare and just plain not contribute. This gets more true as you go further down the income ladder. Crime is actually a luxury: People can afford to turn to crime, drugs, that kind of thing if they know the state will take care of them. In a more capitalist system, people are forced to take care of themselves, and drugs or crime will basically mean that they go hungry.
Counterpoints to prepare against: People who really DO need the support. I've got a couple friends who are on government health care for example, and it's a constant struggle for them to navigate the paperwork just to literally survive. It's a lot harder when you've got a brain injury, too, and if the system was any harder on them they'd be dead. Your right-wing economic model has to distinguish between who needs help and who doesn't ("people who should work, SHOULD work, but just because we're fiscal conservatives doesn't mean we want to bring back poorhouses" or something). How the hell the system is supposed to make that distinction I don't know, that's why I'm not a conservative, but there you go.
And of course, the other side of the argument is that where production and innovation are concerned, the things that a rich guy does to empower himself further are good for society as a whole. Look at the railroad networks: Lots of companies competed very, VERY heavily to lay track fast, to have better trains, because it would make them rich. As a result, the whole nation got a huge and efficient train system. Dodge intellectual property if you can--that means avoiding drug development and early aviation circa WW1--or maybe just say that intellectual property is broken in ways that neither side is responsible for, and you want to fix them too (because if you can claim responsibility for medical developments without getting your ass nailed to the wall with patents and insane USA medical costs, you will do great). Point out that capitalism means competing for contracts, which saves money for the government and reduces waste. Your opponents might claim that capitalists are the ruling elite, but you can counter that someone who does the job better and cheaper can break right in; without a lassiez-faire system you start turning to fascism (where the government gets in bed with its favorite industries).
Also, JP Morgan. He's your hero. In capitalist America, banks bail out the government! Anyway, any time people start whining about capitalist monopolies, ask them if they would have the products and services they currently enjoy if the monopoly never existed. Microsoft? They brought the computer industry to the masses. Phone companies? The government specifically allowed them monopolies in some areas--and in exchange, they developed the area. Wal-Mart? When they build a store out in the middle of nowhere, NEW towns spring up AROUND them. They anchor communities, and lower prices for consumers so they can spend more money on non-essentials to improve their quality of life. Factory farms are more efficient and produce less waste (see, capitalism is good for the environment). Etc.