How often should one submit a site map to Google for a site similar to this?
You really only need to submit it when your site first goes live. After that you should try to keep your site map as up to date as possible so that any time Google crawls your site they will have the latest update to your site. Remember that Google looks for the sitemap.xml file before it looks for general files and pages in your site.
Ideally you should submit a sitemap each time there is an update regarding any page of your site, no matter its size, see section Submitting your Sitemap via an HTTP request within Informing search engine crawlers for the best method to achieve this: a site with a size like this one will likely be served via a Content Management System and any decent CMS should offer do do this automatically for you (at least via a respective plugin or so).
Pinging Google like this about any change as it happens allows Google to determine when to actually download the sitemap thereafter (usually very fast).
On Google I observed that they actually download your sitemap every 2 or 3 days automatically. The only time I'd find logical to resubmit it would be when I add extra pages to the site and obviously to the sitemap.xml itself, although ... theoretically should the site changes be reflected properly in the sitemap.xml we shouldn't really need to resubmit the sitemap (but only upload it) since Google will make the updates automatically. This is more of a question ...
Google I think does download your sitemap frequently depending on the frequency at which it finds any new content from its previous crawl. Having your sitemap submitted daily when new content is added should help your pages get indexed faster.
I would suggest you have a have a cron job or some plugin that automatically pings or submits the individually added or updated pages/links instead of submitting the entire sitemap. Submitting just the new page would probably get it indexed within minutes unlike pinging the sitemap where it might take a day or several before Google even crawls the new link.