There is no definitive answer to the predicament and it would be whatever way you are most comfortable with.
You could change all your logging to write to a central database then create a small program which would scrape this data for you. This method also includes configuring a central syslog server:
http://www.linuxjournal.com/content/creating-centralized-syslog-server
What ever way you want to read these files is fine and all depends how much control you want. You could simply name all the logs based on hostname and rsync
them to a central server from where you could parse them.
There are also free tools out there which will aid you in choosing you method take a look at:
http://www.linuxjournal.com/content/creating-centralized-syslog-server
There are also some proprietary systems you could use, such as Splunk:
This is by no means a definitive list but should aim you in the right direction.