The first step is to decide which one of these two categories your case will fall into. The next step is to have a time period in mind to help narrow down the search even more. Then, check each court having the proper jurisdiction for the time period it covers. Those records not in the desired time period can now be eliminated. While using courts with concurrent jurisdiction, remember to check each series to see if it contains records of a civil or criminal nature.
Lets look at an example.
Your ancestor was arrested in the 1890's , but you aren't sure of what crime. First, you would check the jurisdiction chart, since you know it would be in a criminal court. This eliminates six courts right away. Now, you check all courts with criminal and concurrent jurisdiction to find out which ones cover your time period. By doing this, you narrow down your search to five courts, plus the trial term of the Supreme Court.