Site can be used to expose a VF page to "Guest users" (unauthenticated). It comes with some limits like traffic within 24 hours. Best use cases include exposing Frequently Asked Questions (FAQ) which you manage as Salesforce Knowledge Base but want to show to wide audience. Or maybe a product catalog (although Commerce Cloud or even SIte.com for beautiful marketing stuff comes to mind).
If you expose your VF page as Site - anybody can find it on the net and interact with it. It becomes your job to protect it somehow (share some secret keyword with drivers?) and if you fail - you can get lots of spam records very fast.
It might be better idea to use some cheap license (but then have Salesforce take care of authenticating the users instead of writing it yourself). Maybe Chatter Plus license or Community - a lot depends here whether drivers are really your employees or more like partner company. Are you sure that the only thing they'll ever need to access is few VF pages? How many forms need to be signed daily on average?