Robert Nozick's Anarchy, State and Utopia is a solid philosophical foundation for a lot of right wing thought. If you want to engage further you can follow up with Michael Otsuka's critique in Self-Ownership and Equality: A Lockean Reconciliation.

Nozick provides an underpinning for what many think of as traditional conservative American values, without basing it in Christianity.

Then of course there's the Chicago school of economics (Friedman et al), which is just a somewhat naive and more it less completely discredited take on how the economy works. It's fundamental for understanding American politics the previous half century, but their ideas are not really worth interacting with unless you're particularly interested in economics. It's not like the idiot politicians who push it in front of them understand the theories either.

The theories is not far right; there's no salvaging the far right, and their ideological basis is mostly just bigotry. You could read Ayn Rand to try to understand which hole these idiots crawled from. Or better, don't waste your time.