1) During Install the fmeadmin user will require write permissions on the following directories:

<FMEServerDir>
<FMEServerDir>/Server/fme/licenses
<TomcatDir>/webapps
 
2) The fmerun user will require write permission on the following directories and their sub directories:

<FMEServerDir>/DefaultResults
<FMEServerDir>/Logs
<FMEServerDir>/Server/repository
<FMEServerDir>/Server/database/hsqldb*
<TomcatDir>/ROOT/fmedatadownloadresults
 
3) The tomcat or other web application user will require write permission on the following directories:

<FMEServerDir>/Logs/<serviceSubDirectories>
<FMEServerDir>/Server/upload
 
*Assuming you are using the installed HSQL database and have yet to upgrade to your production database.