Changes to match icssc/docs#33 (#61)

<!--- Provide a general summary of your changes in the Title above -->

## Description

Finishes the work of icssc/docs#33 by:

- Removing CONTRIBUTING.md; this was moved to docs.
- Changing links consistent with that PR.

**Please merge and deploy this simultaneously with icssc/docs#33 to
avoid broken links**.

## Related Issue

Closes #58.

## Motivation and Context

As the issue mentions, the docs could use significant improvements in
organizational clarity and beginner-friendly approach.

## How Has This Been Tested?

No need to test visual changes of this nature.
Corresponding docs pages were obviously tested.

## Screenshots (if appropriate):

N/A

## Types of changes

- [ ] Bug fix (non-breaking change which fixes an issue)
- [ ] New feature (non-breaking change which adds functionality)
- [ ] Breaking change (fix or feature that would cause existing
functionality to change)

## Checklist:

- [ ] My code involves a change to the database schema.
- [x] My code requires a change to the documentation.

README.md

@@ -14,11 +14,11 @@ Anteater API (formerly known as PeterPortal API) is a student-developed and main
 
 ## 🤝 Contributing
 
-We welcome all open-source contributions! Please start by reading the contributing guide.
+We welcome all open-source contributions! Please start by reading the [contributor docs](https://docs.icssc.club/docs/contributor/anteaterapi/).
 
 ## 🧑‍💻 Usage
 
-Take a look at the [docs](https://docs.icssc.club/docs/developer/anteaterapi) and [API reference](https://anteaterapi.com/reference) to get started! **Note that if you use Anteater API, you must give proper attribution in accordance with the [attribution policy](https://docs.icssc.club/docs/developer/anteaterapi/attribution-policy)**.
+Take a look at the [developer docs](https://docs.icssc.club/docs/developer/anteaterapi) and [about page](https://docs.icssc.club/docs/about/anteaterapi) to get started! **Note that if you use Anteater API, you must give proper attribution in accordance with the [attribution policy](https://docs.icssc.club/docs/developer/anteaterapi/attribution-policy)**.
 
 ## ⚠️ Caveats