Clean up and expand readme

[parlough]

• Fix a few minor typo, punctuation, and grammar issues
• Adjust wording for clarity
• Add more cross links to Flutter, Firebase, and package docs where relevant
• Add alt text to screenshot and make it a link target as well
• Adjust sections of text that are links
• Use Markdown and GFM features where appropriate (ordered list, warning blocks, etc)
• Add some line breaks and separate link definitions for easier editing and review
• Update comments in code blocks to more closely follow Effective Dart
• Adjust placeholders (...) in code snippets to be in comments to make them directly copyable
• Other misc and minor adjustments

[csells]

When I preview the updated README in this PR, the paragraph flow is gone and all of the lines are unnaturally shortened:

[domesticmouse]

Please resolve conflicts =)

[parlough]

When I preview the updated README in this PR, the paragraph flow is gone and all of the lines are unnaturally shortened:

This is intentional to use semantic breaks for making editing and reviewing raw Markdown easier and more intentional.

Markdown renderers join lines with spaces so these awkward previews won't show up in most cases, but it seems the VS Code preview you're using doesn't handle that properly. You can see in the GitHub view those line breaks don't appear.