It's actually quite a huge undertaking, but well worth the experience. Here are just one or two suggestions...
Site security also means being heavily involved in managing your sometimes scarce resources. Just as important is obeying any limits your host has, and guessing all possible ways your site users can push you over those limits, leaving you responsible to pay a hefty bill. IE downloading or uploading large files over and over, spamming email lists, repeatedly requesting pages using too many database connections and queries, etc. Get overusage limits and fees in writing from your host before you begin, and have response plans ready. Really, this part is like buying a cellphone service.
A lot would also depend on what features you'll have on your site. File uploads? Forum? Logins? Email? Etc? For example - If you're running a file-sharing site: along with upload/download rate limiting, I suggest you first check available disk space before permitting any file to be uploaded, or do regular audits so you're prepared to archive or delete old and unused files. It's a quick check just to make sure you're not caught by surprise a year down the road when you suddenly start getting disk full errors or get shafted by your host with a large bill.
There are literally a hundred more issues to consider. Gather up a complete overview - an itemized list - of all features and functions of your site. Google each one to get more ideas on handling security. Your host should also publish their own security considerations and have a handy manual for operating with all of their services. If they don't, well, I wouldn't personally feel comfortable with them.