Best way to typeset micrometers?

The siunitx package does this 'properly' without the user needing to worry

\documentclass{article}
\usepackage{siunitx}
\begin{document}
  \SI{1.55}{\micro\metre}
\end{document}

(Note: I am the author of siunitx, which is the successor to both SIunits and SIstyle.)

Of course, for the more general question about upright Greek letters then the upgreek package is indeed the best plan.

Joseph Wright’s answer is correct, but I’ll give a more comprehensive list. As of 2020, \textmu is defined by the LaTeX kernel. You can therefore write, 40~{\textmu}m in text mode, or just 40~µm, where µ is U+00B5. On LuaTeX or XeTeX, you can also write ~{^^^^00b5}m. (You normally want the space between the number and the unit to be non-breaking.)

If you are compiling with PDFLaTeX on an installation older than TeX Live 2020, you will additionally need \usepackage{textcomp} for this to work. On LuaLaTeX or XeLaTeX, you would use fontspec.

Within math mode, you can wrap any of these in \textnormal.

In practice, you would end up defining some kind of \um or \micrometer command that’s no easier than using siunitx, e.g.

\newcommand\textmicrometer{~{\textmu}m}
\newcommand\micrometer{%
\ifmmode\textnormal{\textmicrometer}%
\else\textmicrometer%
\fi}