Please tell me some basic tips on keeping my website secure from hackers, spammers and the works?

Make sure that you keep the password strong. Most of them use simple passwords to memorize it easily. But this would actually the ease the work of a hacker. Also to make sure that you avtivate SPF records, Domain keys,....to keep spammers away from your account. (But actually none of these methods won't prevent from spamming attack.). You can either depend on some third party antispam service providers for this.....Another way is to deal each kind of spam by checking any common properties all these spams & then create a filter for your account to discard all mails with this feature....
hope this is clear...let me know if you have any doubts.....

Thanks,
Tony