Ok I'm going to go ahead and give my thoughts on this. There is no ultimate 'best font' nor can there be because choosing a font depends on many different aspects. What there can be is a 'best method for choosing a font'.
So things to consider to help choose the best font for your project;
Media: How will the font be displayed, paper, canvas, online, portable device, etc. You want to make sure that you are choosing a font appropriate to the media that it will be displayed on, for example a block of Times New Roman might be fine for a printed document but, on screen (especially a small screen) a block of Times New Roman can be quite difficult to read. You also want to see what is available to you if you are restricted to web fonts, resources such as google fonts could help you out here.
(From Wikipedia: "Web Safe Fonts
Web-safe fonts are fonts likely to be present on a wide range of computer systems, and used by Web content authors to increase the likelihood that content displays in their chosen font. If a visitor to a Web site does not have the specified font, their browser tries to select a similar alternative, based on the author-specified fallback fonts and generic families or it uses font substitution defined in the visitor's operating system.")
Audience: Think about who will be reading it. A young child might do better without a serif based font, or a single story 'a' as opposed to a double story 'a'. However if it were say a wedding invitation then fonts such as Edwardian Script are what's highly popular in that context because let's face it the more Serif, the more decorative the better - according to some brides that is ;) though even still the decorative stuff is used primarily for titles rather than entire content. As a wise ol
Contrast/Colour: Again this is something to consider in terms of your project. Of course you don't want to blind people as a result of terribly high contrast, or give them wrinkles from squinting at something that has terribly low contrast - that part is obvious. But depending on your colour scheme you might want to fiddle with brightness and contrast settings. You'll notice that GD.SE for example is not completely black and completely white (as asked & answered here)- it has a lower contrast than that, consequently it's quite easy to look at this website for very long periods of time by comparison to looking at something with a much higher contrast- your eyes would get tired!
Weight: In general lighter weighted fonts ten to be a little more legible than some heavier ones, this is discussed further here along with other aspects of legibility which you may find useful.
How many: Depending on your media, audience and content you might want to choose several fonts. Of this I suggest being wary. You most certainly do not want to confuse the content. The whole point of font is to communicate something, what you are looking for is the way to do that most effectively. Too many fonts can be confusing,though a single font can sometimes be boring. Generally mixing it up in terms of bold/italics and size with maybe two fonts is what tends to happen. Pairing fonts is discussed a little more here.
These are some of the aspects that you should narrow down if you are going from a blank slate but though there is a lot to consider when it really comes down to it, it's not that bad. The value of choosing the right font/fonts at the early stage of a project has no comparison! There is more about factors to consider while choosing a font here.
A good analogy is that it's like getting dressed, a simple concept that is discussed here.
So as the format of my answer naturally fell, you want to first figure out who it is for and what it has to say - then you want to figure out the means of communication, which font :) and since this wouldn't be a Jenna-Answer without an abundance of links, this is further discussed here.
I strongly suggest reading the links that I have provided, they are quite helpful and will help to equip you to choose the right font for your project, this is what will improve the reader experience. It is not just about the legibility but also the entire context that the font is contributing to, not to mention the aesthetic an adequately legible font might take away from a design entirely when and equally legible but more appropriate one might go unnoticed and therefore make the design and the information the most prominent things. Taking time to do this in my opinion is quite essential.
Hope I've helped and haven't rambled too much, I am a little passionate about the right font :) Good luck with your project.