The only real requirement here is that the USER that Apache runs as (usually "apache" or "nobody") needs to have WRITE access to most of the directories in the site. This is so that PHP can write uploaded files to the proper directories without problems, and so the installer can have access to creating necessary files during installation.
The easiest way to do this is to set the GROUP owner of Manifesto to a group that includes the Apache user, and to allow the group to have WRITE access to the appropriate directories.

The recommended method is this. These commands should be executed as root:

1. cd to the Manifesto directory you just extracted, e.g. cd Manifesto
2. Create a new user on your system, called imcuser. When creating the user, make its default group a group with the same name.
   e.g. useradd imcuser
   If you need to create the group, groupadd imcuser
3. Add the Apache user (apache in our example) to the new group imcuser.
   e.g. usermod -G imcuser apache
   (beware that, when using the "-G" flag, you must specify ALL supplemental groups that user belongs to. If you omit an existing supplemental group, the user will be removed from that group. So you may need to do e.g., usermod -G imcuser,othergroup,thirdgroup apache)
4. The directory root and all subdirectories should be owned by imcuser, group imcuser.
   e.g. chown -R imcuser:imcuser . ./*
5. Permissions SHOULD still be set properly for all directories and files from the tarball. The rules are as follows, if you wish to confirm:

   Default permissions for files should be 0664 (read/write for owner and group, read-only for world)
   They should look like this:
   

   -rw-rw-r-- 1 imcuser imcuser 4538 May 5 23:34 index.php
   -rw-rw-r-- 1 imcuser imcuser 1710 May 5 23:34 info
   -rw-rw-r-- 1 imcuser imcuser 4830 May 5 23:34 info.inc
   

   To modify all the files: find . -type f -exec chmod 664 {} \;

   Default permissions for folders should be 2775 (read/write for owner and group, read-only for world). The Apache user must have write access to all directories for installation, but after it's installed, if you wish to be a bit more restrictive, the Apache user normally needs write access only to

   cache
   cronjobs (and subdirectories)
   images
   usermedia (and subdirectories)
   docs
   

   But if you want to run the Auto-Update module, Apache needs full write permissions to everything in the root and subdirectories, since it needs to replace files.
   The default permissions should look like this:
   

   drwxrwsr-x 7 imcuser imcuser 4096 May 4 14:15 usermedia

   
   To modify all the folders: find . -type d -exec chmod 2775 {} \;