I'm certainly no expert on American conservatism, and what conservatives in general do and don't stand for, but what conservatism means to me is that we should be as skeptical of big business as we are of big government (I suppose in the vein of Teddy Roosevelt), and for many of the same reasons, as big business has the potential to become tyrannical just as big government does. And the way to practice that personally is through supporting businesses that are small and local and independent. On a policy level, it seems like conservatism have become synonymous with Ayn Rand libertarianism, which doesn't seem right to me. I don't think it is a traditional American conservative position (see Russell Kirk) that the free market and business should be allowed to run amok, unfettered and unchecked by regulation. Rather, I think traditional American conservatives would believe that there is an important role for government (federal and local) to play in checking big business, to ensure as level a playing field as possible and to make sure they aren't doing things like ruining our rivers and air with no recompense. And that government impose those checks when necessary through regulation and through the antitrust laws. I think the problems conservatives have (or should have) with government regulation is that they often result in making the playing field less level because a small family-run farm can't afford to put in handicap accessible bathrooms for its non-existent employees, or whatever. Big business uses these regulations to increase barriers to entry and stifle competition.
On the government side, I don't think it's necessarily accurate to say that conservatives are always for lowering taxes. I think there's some nuance there. I think it can be a conservative position to say that the federal government has gotten too big and has way too much control over our daily lives in a way that does not create healthy and productive communities, families, and individuals. And so we should be in favor of giving the federal government less of our income. Conversely, I likely would be totally in favor of redirecting those federal tax dollars (and even sending more of my tax dollars) to state and more importantly county and municipal governments. Because I can vote with my feet and choose to live in states and municipalities that use public money wisely in a way that does in fact create healthy and productive communities, families, and individuals.