If you are trying to build an authority blog with a lot of content, you should pick a niche that you are passionate about. This will allow you to create content on a consistent basis and be able to provide value to people. Google loves high quality content and tends to rank sites well that have great content. However, if you are trying to make small niche sites, then your focus should be on problem solving markets where people buy products to solve their problems. Most people try to rank for product names, but it is also possible to make money by finding problem related keywords and creating websites that sell products to solve the problem.

This question is impossible to answer without knowing a whole range of others things about what you plan to do (eg. how do you plan to monetize the site, what kind of content are you going to have, what kind of competition level are you comfortable competing with in the SERPs? etc.)

The ultimate niche is one not being catered for. Every bloggers dream.

Depends on what you like to do? Writing content? Write a website on PHP/MYSQL? You also have to think about many things like how much time can you spend, what would you like to do with your website now and ... for example after 1 year... and many many other things!

The best niche is a subject you already know.

Everyone knows things other people would like to know. So find a way to monetize what you already know.

Make a site based on your interest. Try to put affiliate links, although this in not 1 sentence solution. you need to study alot of things before you step-in a affiliate business. (It seems to me monetizing blogs for earning money you trying to mention that you are interested to do some affiliate business.)
Your known topic is good anyway.

Always go according to your interest, if your interest in health topics, create a blog related to health, it should help in earning money.