Ironic that you find Century Schoolbook suitable for online documentation, as it was developed nearly 100 years ago for school textbooks!
While googling I found esperfonto, which has a search box to help pair fonts.
They suggest Arial, Helvetica, or Frutiger Humanist 777 for sans fonts. They don't suggest monospace pairs, though.
The Frutiger family is not free. I tried Century Schoolbook, Helvetica, and Courier, and it seems to look pretty good.
Here is a sample document (requires xelatex) to test your selections:
\documentclass{article}
\title{Font Test}
\usepackage[english]{babel}
\usepackage{blindtext}
\usepackage{fontspec}
\setmainfont{Century Schoolbook}
\setsansfont{Helvetica}
\setmonofont{Courier}
\usepackage{sectsty}
\allsectionsfont{\sffamily}
\begin{document}
\maketitle
This article uses the \textsf{blindtext} package to typeset dummy text. The preamble is:
\begin{verbatim}
\documentclass{article}
\title{Font Test}
\usepackage[english]{babel}
\usepackage{blindtext}
\usepackage{fontspec}
\setmainfont{Century Schoolbook}
\setsansfont{Arial}
\usepackage{sectsty}
\setmonofont{Courier}
\allsectionsfont{\sffamily}
\end{verbatim}
\blinddocument
\end{document}