I was introduced to Austrian economics via Supply-Side economics, which has a great respect for the Austrians. The Supply-Siders I learned from (mostly the Wanniski branch as opposed to the Mundell or Laffer branches, though I did study with Mundell at Columbia) were constantly quoting Mises and Hayek (but not Rothbard).
The difference between Supply-Side and Demand-Side economics is that Supply-Siders think that production drives the economy and Demand-Siders think consumption drives the economy. Thus, Supply-Side policies tend to focus on things like tax cuts, decreased government spending and a stable currency (i.e. one tied to gold, though not necessarily convertible to gold) to stimulate the economy, and they oppose Demand-Side policies which tend to promote tax increases, increased government spending, and credit expansion to stimulate the economy.
The difference between Supply-Side economics and Austrian economics is that Supply-Side economics is a utilitarian, ends-based framework, while Austrian economics is a morally consistent, means-based framework. For example, Supply-Siders think high taxation is inefficient (using the Laffer Curve as their theoretical basis); Austrians think any taxation is evil robbery. Supply-Siders think the state can work fine, if only producer-friendly policies were pursued; Austrians obviously are enemies of the state.
When I attended Mises U. in 2005, I was still half Supply-Sider, but I’m a full on Austrian now.