Sans serif font with distinguished capital I for math.

Relative newcomers to the TeX world are Google's droid fonts, but a package was recently put on CTAN. It has the feature you want for capital I.

\documentclass{article}
\renewcommand*{\familydefault}{\sfdefault}
\usepackage{droid}
\begin{document}
\Huge This is droid sans. I like it. 
\end{document}

No swish on i or l, but j does.

This is an old question, but it's exactly the question I have today. I'm not sure if Droid now has a true italic, but it's worth noting Noto Sans:

It is based on Droid, and there is a corresponding serif. Probably this is old news here, but the Noto project's "design goal is to achieve visual harmonization (e.g., compatible heights and stroke thicknesses) across languages", with planned coverage for "all living scripts in Unicode by the end of 2014". (Note 2,410 glyphs in the Font Squirrel version.)

I suggest iwona.

Test:

\documentclass{article}
\usepackage[math]{iwona}
\begin{document}

lmnLMN-IJKijk

$lmnLMN-ijkIJK$

\end{document}

See also http://www.tug.dk/FontCatalogue/iwona/