What salary will you be earning in Hungary?
The answer to your question regarding cost of living in Hungary depends entirely on your lifestyle and the standard of living you are accustomed to. The best thing I can suggest is to draw up a rough list of your typical monthly expenses and use tools such as Expatistan and Numbeo to get the costs of common expenses. Then plug the numbers you find there into your list, add them up, and you'll have an estimate of how much money you'll need.
Bear in mind that cost of living can vary slightly depending on where in Hungary you live. For instance, living in the capital, Budapest, will be more expensive than living in a smaller town or city. For a broad idea of common expenses, please see our page on Cost of Living in Hungary.
Best of luck with your move.