Hello There,
I can Install and configure auditing tools on your Linux server for auditing File Changes, User activity (auditing) and such.
Also, Configure your "syslog" to write on separate server or destination.
About Bid's price, It will take 3 - 4 hours to install and configure systems properly so It's not possible to do the job with your mentioned Project budget. $100 is quite reasonable :)
Best Regards,
Daniel Gordi