Does the ‘reset’ option erase my phone? Or should I manually erase things?

You should use the following instructions if you want to completely erase everything on your iPhone, such as when you are selling or giving it away: What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Manually erasing thing can also erase things synced with iCloud such as iCloud Contacts, iCloud Photos, etc. while the above instructions will not.