The main belief, at least the one they’re willing to state plainly, is phrased as “small government”.
Upon further analysis it becomes that the definitions of “small” and “government” have no real objective meaning; they’re more intended to express sentiments about the role of government. “Small” means “carries minimal tax burden”, and “government” tends to be measures intended to promote the general welfare.
If we’re talking about the size of the military, no size or expense is considered “small”, the expenditure is judged to be appropriately sized because it serves conservatives’ favored ideas about the role of government. You can see a similar disparity in sentiment toward military aid to some countries (i.e. South Korea) and opposition to others (Ukraine), none of that is related to the size of the expenditure, it’s all about ideological alightment.
OTOH the Department of Education only consumes a tenth of the DoD’s expenditure, yet it’s considered massively over-bloated because conservatives hate what that department represents. Conservatives would prefer to have education responsibilities devolved on the states so that certain states can neglect, corrupt, or entirely ignore such responsibilities.
Which brings us to the other tenet - a commonly expressed rationale for this is “states’ rights” or “local control” which is often flatteringly portrayed as a desire for states to be a laboratory to learn which policies work and don’t work, but in reality tend to be a strategy for states to determine the minimal number of civil rights they can get away with extending to their residents.
The canonical example of course is slavery, a war on human rights which was (and still widely is) justified under the banner of “states rights”. Chattel slavery is of course gone, but looking at the status of civil rights, economic achievement, and quality of life in the more right-wing states, we can see that “states rights” is usually a vehicle for certain states to unequally restrict the rights of some of its citizens. Though slavery is declared unconstitutional (adjudicated by combat, it must be pointed out), former slave states have never given up on the project of inequality and apartheid, and the doctrine of “states rights” or “states sovereignty” is understood to the the theory required to achieve this.
I of course have little idea what conservatives actually believe, because they cloak their intent in the transparently obvious ruses described above. They understand that their intent must be obfuscated because it recruits little support when stated openly (at least prior to 2016). I suspect they have no consistent inner beliefs except for their own right to power and privilege. But “small government” and “states rights” are how American conservatives tend to describe their beliefs.