The short answer is anything you can get your hands on. Most of us have mobile phones and most of us could use just a mobile phone video to produce decent enough VLOG footage, however paying that bit extra for a proper setup will help your shots look better but also allow you to get better sound (a must for anyone serious about VLOGGING)
The FIRST thing to remember is it’s not just the equipment you own that makes you a good or bad VLOGGER, it’s the content you create.
Make awesome content that people want to see more of and you can just continue on your old iPhone or Android phone but at points you will want to upgrade for various reasons, e.g. average sound, poor low light, sharpness of images etc
The most important thing that lots of people forget about when starting is your audio, get an external mic if possible or at the very least just sit and listen to your footage and try and improve it on post-production.
Casey Neistat Setup (one of the best visual VLOGGERS):