LaTeX fonts with math and utf8 support

Question

Although I like Computer Modern font families I'd like to be able to make documents look like they were made by "normal person" and still be able to benefit from the TeX powers*. In short the solution must fullfill four simple requirements:

1. Cover same font characteristics both for math mode and regular one.
2. Cover glyphs beyond ASCII table correcly.
3. Support luaLaTeX and optionally XeTeX.
4. Cover serif and sans serif faces with all faces (regular, semibold, italic).

Simple requirements but hard to accomplish, though.

So far I am able to fulfill all points with default Computer Modern font failing the zeroth one.

I can also fulfill the points except #2 by using fonts from this site, say:

\usepackage[utf8]{inputenc}
\usepackage{arev}
\usepackage[T1]{fontenc}

and I've identified the T1 encoding to be responsible for the limitted support.

I can also fulfill the points except #1, the math font is Still Computer Modern Roman:

\usepackage[utf8]{inputenc}
\usepackage{fontspec}
\setmainfont{Arial}[
UprightFeatures = { SizeFeatures = {
{Size=-10, OpticalSize=8 },
{Size= 10-14, OpticalSize=10},
{Size= 14-18, OpticalSize=14},
{Size= 18-, OpticalSize=18}}}
]

Testing sentence is: Příliš žluťoučký kůň úpěl ďábelské ódy. Feel free to add other dummy sentences if you've found occasions where czech typesetting was correct while the other was not.

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* That means user unfriendly interference with styles, easy splitting "Style definitions" part from the Content part, output stability, stable counters, easy referencing and many others. In short, all the little features we like in (lua)LaTeX.