I am writing a short book. What is the best font size to use with Times New Roman: 12 or 14?
I don't think there is one answer. However, I would definitely caution against using 14 point unless it is for children or the very elderly.
Font size varies according to the type of book and the target audience. I suggest that you pick up a couple of books similar to the one you want to publish and look at the first few pages. Often they list the font name and size.
Otherwise, you could print out a page with various sizes on it and compare it.
Different self-publishing tools have different formatting software. So, it depends entirely on what tool you use and what size you want your finished book to be. If you are planning for your short book to be 8.5 x 11, then consider using a more standard font that you would use for another kind of document.
However, if you are planning on having your finished product being a more standard book size like 5.5 x 8.5, then you will have to consider how the website you’re using formats those books. The website I have used to self-publish books of that size gives me the option to upload a PDF document and use that as the pages in the book. When I do that, it scales down the 8.5 x 11 pages of the original document to fit on the smaller book page size.
If the self-publishing tool you are using does the same, you will need to use a larger font for your text to still be comfortably read by even people with 20x20 vision. I normally use size 18pt or 20pt because of that. But, you will need to take a look at the tool you are going to use and choose a font size accordingly.