Update contributors quick start guide

[IlaiGigi]

This PR focuses on updating and formatting the contributors quick start guide.

As a new experimenting contributor, I had some troubles when I worked with the quick start guide, some commands that didn't work because of outdated packages, some instructions were unclear etc.

Addressing major changes I did:

1. Moving down the installation of the docker compose plugin: If we already have a section that is dedicated to the installation of docker compose, then commands that are relevant to its installation should be there, and not in a section that is dedicated to the installation of purely docker.
2. Sqlite -> sqlite3: according to the Ubuntu package repository, the package sqlite is available only on focal and jammy Ubuntu distribution codenames. This means that the command sudo apt install sqlite will not work with any distributions beyond other than these two (like oracular, noble etc.). As I see it, these are the options:
   a. Move to sqlite3. This would require performing tests, which I have - ran all the tests under the ./tests directory, which is probably not sufficient.
   b. Add a note excluding distributions other than focal and jammy to use sqlite3 instead. This means developing on machines with distributions other than these may lead to inconsistencies as a result of breaking changes between the versions unless compatibility checks are done.
   This is very likely larger than my PR, and the best course of action for now is probably to delay this change until a decision is made, I made the changes only to raise awareness.
3. Removing section describing pre-commit with uv (lines 466-479): this content was just duplicated with the few lines below it. There are more examples of this behavior, but they are less aggressive so I decided to leave them be.

The other changes I made are mostly cosmetic.

[boring-cyborg]

Congratulations on your first Pull Request and welcome to the Apache Airflow community! If you have any issues or are unsure about any anything please check our Contributors' Guide (https://github.com/apache/airflow/blob/main/contributing-docs/README.rst)
Here are some useful points:

• Pay attention to the quality of your code (ruff, mypy and type annotations). Our pre-commits will help you with that.
• In case of a new feature add useful documentation (in docstrings or in docs/ directory). Adding a new operator? Check this short guide Consider adding an example DAG that shows how users should use it.
• Consider using Breeze environment for testing locally, it's a heavy docker but it ships with a working Airflow and a lot of integrations.
• Be patient and persistent. It might take some time to get a review or get the final approval from Committers.
• Please follow ASF Code of Conduct for all communication including (but not limited to) comments on Pull Requests, Mailing list and Slack.
• Be sure to read the Airflow Coding style.
• Always keep your Pull Requests rebased, otherwise your build might fail due to changes not related to your commits.
  Apache Airflow is a community-driven project and together we are making it better 🚀.
  In case of doubts contact the developers at:
  Mailing List: [email protected]
  Slack: https://s.apache.org/airflow-slack