I'm sure there are various tools available that you would install to your server (CSF, RootKit Hunter, etc. to name a few for linux), but if you're in doubt, then I would ask your host for some assistance 😉
Good place to start is to make sure you escape anything entered by a user such as post/request/get. You can use htmlentitites which will change " to \" for you. When inserting anything into mysql put it through as mysql_real_escape_string.
Basic - have a difficult root password. Change SSH port away from 22 to try stop bruteforcers. Don't run things under the root user unless it's necessary.
But I would say the most important is anything user inputted just make sure it's escaped otherwise they could grant themself root, view all database records, delete database, edit files, see passwords, etc..