Updating drupal core manually from 7.0 to 7.78 in one fell swoop

I have recently become an admin for a site that has not been updated since 2011. there are broken links (internal links to the site’s blog go to page not found, index error.) I think this is due to a bug, so I want to update the software. However this would be a manual update of Drupal Core and I’m wary of doing anything that might mess up the site’s code, not being a coder myself.

Should I go somewhere in the middle of the 7.x updates, or should I go straight to the latest one? What issues may arise from my site from updating to the most recent available?