microtype settings for dummies

A number of answers:

Firstly, microtypography is (in my book) the art of enhancing the appearance of a document while exhibiting the minimum degree of visual obtrubsion, that is, ideally, without even being recognisable: Characters with less optical weight should slightly protrude into the margin to make it appear more even, but they shouldn't stick in your face; fonts may be distorted ever-so-slightly to allow for better line breaks, but they should not look distorted. Therefore, it is actually good that you don't see any difference. You should, however, make sure that something does indeed happen: for protrusion, find a hyphen at the end of a line and check whether it protrudes, as it should do, into the margin (by about half of its length), or whether it is fully contained in the text block; for expansion, check whether line breaks in a longer paragraph change when you remove the lines your colleague added. If line breaks are the same in both cases, and if hyphens don't hang over, then protrusion and expansion are in fact not enabled at all, which would be a topic for a new question.

Secondly, the microtypepackage tries to lift the burden of deciding about settings as much as possible from the user. Considering that you say yourself that you are not a man of the finer arts, I would advise to just load the microtype package without any options at all. (In your code, the protrusion and expansion options are superfluous as they are enabled anyway, babel doesn't have any effect, only final may be justified to ensure that line breaks don't change when adding draft as a class option.)

Now for the final point, which obviously causes the most confusion. As Jörg has pointed out, you are using both the microtype package as well as lualatex's own microtypography feature (with the latter taking precedence). You should therefore decide, and either load microtype:

\usepackage[final]{microtype}
\usepackage{fontspec}
\setmainfont[Numbers={OldStyle, Proportional},
             Ligatures=TeX
            ]{Brill}

or use lualatex's techniques:

\usepackage{fontspec}
\protrudechars=2 % or \pdfprotrudechars=2 and
\adjustspacing=2 %    \pdfadjustspacing=2 with luatex < v0.85
\newfontfeature{Microtypography}{protrusion=default;expansion=default}
\directlua{fonts.protrusions.setups.default.factor=.5}
\setmainfont[Microtypography,
             Numbers={OldStyle, Proportional},
             Ligatures=TeX
            ]{Brill}

I would advise to go with the first, as microtype's settings are more complete and balanced IMHO (but then, I am, of course, biased ...). The second option has the advantage of better integration with luatex. Here, a factor of .5 seems reasonable (the default protrusion, especially of the hyphen, is just too much, quite obtrusive and therefore contradicting the idea of microtypography to me).

I think that defaults are just enough for most texts, but it depend the overall text format (font size, font type, text width, margins, columns, etc.) and how sensitive are your eyes to bad spacing or the abuse of microtype methods.

To test if your settings are OK first try (with some long text) a disproportionated value in one option as stretch=1000. You surely will notice a very strong stretch effect that ruins your text. All right, it was only to see the effect.

Now try successively with much more moderate options (100, 50, 40 ...). When you reach a value (suppose that is 30) where you cannot notice the stretch effect and the text just look good probably you have found a good value. It is time to check finally if there are some difference within you election and the default (20) or even less (For example, some people find 10 more appropriate).

In a editor as Gummi you can see the changes in the PDF in about one second, so this check is faster than it looks.

It would also be advisable to look on Google to see the options that people choose. After all, the document should not be attractive to the author but to target readers.