issues effecting federal lands and national parks
The majority of cases in the US are heard by the various state courts.
Courts that have the authority to be the first courts in which most federal cases are heard are known as district courts. These are the trial courts of the federal judiciary system and are responsible for hearing both civil and criminal cases.
Traffic cases are heard in traffic courts. Sometimes, these limited jurisdiction courts also hear low level misdemeanors.
Federal courts may hear civil cases or criminal cases.
murder
Crimminal and Civil cases.
Cases where the decision hinges on the application of a constitutional provision are heard in Constitutional Courts. A good example of such cases would include all cases concerning Freedom of Speech as guaranteed in the First Amendment.
lower district courts
Appealed
Lower courts are where cases are initially started. If they are appealed, they are taken to higher courts.
The appellate court with jurisdiction over cases heard in the relevant trial court.
The states divide jurisdictions between state courts in their own manner. Where I live, felonies are heard in superior court and misdemeanors are heard in another court.