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 =)

[domesticmouse]

🎉