HOLY FREAKIN' VIRUSES!!!

Short story:

1. Last week I learned I had viruses (one caused google search results redirected my website to virus websites…but it appeared there were many others).
2. I delete entire website via FTP (removing all viruses)
3. Re-install WordPress
4. Next day I am notified by plug in “Antivirus” that I have many viruses.
5. Two days later I am back to square one, with google redirecting my site to virus-laden websites.

Sooo…How do I stop this from happening? When I do a re-install, is there a file I can change/delete? Change hosting providers (currently Bluehost) I have already changed all my passwords.

Any and all help is greatly appreciated. If there are steps to follow, please let me know what they are in “layman’s” terms.

Thank you, Thank you, Thank you,

Phil
(School Teacher)