Hi Rosie
Thanks for explaining this to me ... I would forget about manually deleting logs and let's concentrate on what can be done to clean up your mac, second hand or other it doesn't matter, it's all down to "what am i going to use this mac for?"
So, think about that and post back what sort of user you are going to be ... just emailing and web surfing? Are you going to use iPhoto to manage your digital photos ... do you have a video camera and will be using apps like iMovie or iDVD? What are your hobbies and how can you best use your mac to take them that little bit further?
Does the mac have more than one User Account? We have to know this because it's wise to have at least 2 accounts, one Admin acct and the other one a Standard acct which you will use for every day use. If you go into System Preferences ~> then click on Accounts (in the System section) you will/should see your account type in the left hand box in the new window that opens.
If there is already an Admin acct, then do you know the password? Down in the bottom left hand side of the same window you will notice a padlock ... the padlock may be unlocked or locked. Either way, you need that password.
Also, do you have the System Install Disc/s that came with this mac? You are going to need them sooner or later so we can deal with that later.
You are correct with OnyX advising you to Back-Up your data and files before using the app ... to be perfectly honest I don't run OnyX that often because my iMac is running fine for me. When I do run it, I run it from my Admin acct and don't touch my iMac while OnyX is doing it's thing. BTW, OnyX as do other maintenance apps for Mac OS X, will clean up your logs for you.
I strongly advise to forget OnyX for now and let's see what you have installed and what the next step is.
Have a look through your Applications folder for any apps that you think you are not going to need. Don't delete anything yet until you post back about them ... in the meantime, download and install this clean up app that is useful when we are deleting an app as it helps to gather up all the sundry cruft that is otherwise left behind when an app is deleted.
AppTrap