I was libertarian, looking at Democrats and Republicans, and living in a state that allowed voting for even judges.
I'd vote Dem for criminal law positions: criminal judges & prosecutors. I felt like the GOP was more likely to go after people selling sex toys and such, which I thought was silly and a waste of government resources. I figured the really bad offenders (thieves and murderers) would get prosecuted and jailed no matter which party was in charge. (I don't think that now, though. Granted, it depends on the candidate.)
I'd vote GOP for fiscal responsibility and positions that affected businesses: legislature positions and civil judges. I felt like the Dems would impose silly and wasteful restrictions on businesses and waste tax money generally. (Now, both parties waste money.)
I'd vote Libertarian when I wanted, especially if it was a race that was calculated to keep the Lib party on the ballot (one candidate in a statewide race would have to get a certain percentage to be on the ballot the following year automatically).