What is the best way to create quiz website?

While there can be multiple answers for this and quite a few of them would be the right. The best however - is for you to decide based upon your preferences.

As someone who likes to quiz - I would basically like a good old fashioned blog. It has questions. It has answers. If it has a little bit of trivia associated with stuff which is interesting and / or form a good question - it is GOLD.

Here is what I suggest that you do.

1. Register a good domain name via Godaddy and get some hosting space via them as well. They provide wordpress integration which makes the job whole lot easier.
2. Choose a wordpress theme which is easy on the eyes. Not too flashy but something that makes it easy to read.
3. Make at least two posts every week - one on current affairs and one on anything else that you find "interesting". Do keep in mind that most of your audience is going to be interested in quizzing.
4. Have a guest post option so that anyone who wants can contribute to the website. You can approve or reject the post based upon the content.
5. Have a calendar widget / app integrated on the website that has information about upcoming quizzes. People should be able to submit the information about upcoming quizzes.

If you can implement these five steps, I believe you will have a killer website and at least one loyal user who visits it regularly. Hope it sees light of the day. Also, if you need any sort of further help in making this a reality - do get in touch with me. I will be more than happy to contribute in some way or the other.