That’s a tricky but fundamental question! First you will define how much you require! The average budget of a world tour for a year is between 15’000 and 20’000 EUR. Of course this will depend on your destinations and on the length of your trip. More information here on how to do your budget.
Your own money
Make sure to have more than needed rather than just the amount, as people tend to minimize their budget and end up struggling. Having more doesn’t mean you should spend more! But it would provide you with a safety net in case of unexpected events!
Be careful to also have some money saved for when you return. If you have quit your job, it might take some time to find a new one and you will need some savings to survive a few months.