What are the best resources for a non-programmer/beginner who wants to learn LaTeX?

The Lyx editor (http://www.lyx.org/) is a nice way to get started, as it will get you writing and allow you to see the underlying LaTeX as you go. If you are writing regularly and using LaTeX for the formatting and presentation, you could get up to speed on the basics in a couple of days.

For building equations, sometimes it helps to start with something visual - this online tool is fantastic: http://www.codecogs.com/components/equationeditor/equationeditor.php

I only use LaTeX these days when I want something to look typeset or if I need to present a formula that actually looks right in context and that will scale (otherwise a picture (bitmap) is just as good).

Use Pandoc instead. Write your document in markdown and pandoc will convert it to LaTeX, HTML, Open Office, PDF, ePub, and more. For mathematics, write the formula in LaTeX, and Pandoc will know what to do with it.

[Markdown] is much easier to learn than LaTeX, and less distracting too. Plain markdown is supported all over the web (the comment boxes on this site use Markdown to format these comments). Pandoc's [extended markdown] supports everything you need for serious writing: footnotes, definition lists, citation processing, LaTeX math and LaTeX macros, tables, and more.

LaTeX [touts itself] as a system that allows writers to focus on content. Here is the example from that page in LaTeX:

Cartesian closed categories and the price of eggs
Jane Doe
September 1994

Hello world!

Here is what you'd have to write to get that in LaTeX:

documentclass{article}
title{Cartesian closed categories and the price of eggs}
author{Jane Doe}
date{September 1994}
begin{document}
   maketitle
   Hello world!

end{document}

Here is what you'd write to get that in Pandoc:

% Cartesian closed categories and the price of eggs
% Jane Doe
% September 1994

Hello world!

More generally, LaTeX forces you to constantly litter your text with begin{foo}s and {bf ... } and the like. By contrast, text written in markdown is clean and easy to read, even if you have no idea what markdown is.

Of course, you'll still need to learn LaTeX for writing formulas. But unless you need to do things that are seriously complex, that is fairly straightforward.