What is the recommended way for using PHPUnit?
drupal/recommended-project doesn't install PHPUnit, which is instead installed with the drupal/core-dev meta-package. For example, if I wanted to install Drupal 9.0.3, including PHPUnit, I would use the following commands.
composer create-project drupal/recommended-project:^9.0 my-project
cd my-project
composer require 'drupal/core-dev:^9.0'

As said in Starting a Site Using Drupal Composer Project Templates / Adding drupal/core-dev, drupal/core-dev still doesn't depend on drupal/core. Specifying a version of drupal/core-dev is necessary to get a version that matches the Drupal core version you are using.
Also, if you want to install Drush, you need to first install drupal/core-dev and then drush/drush.
As for the PHPUnit version, drupal/core-dev 9.0.3 requires the following packages.

phpspec/prophecy: ^1.7
phpunit/phpunit: ^8.4.1
symfony/phpunit-bridge: ^4.4

Using more recent version for phpunit/phpunit and symfony/phpunit-bridge hasn't been tested, yet.
For Drupal 8.8.0, drupal/core-dev 8.8.0 requires a version of phpunit/phpunit
that matches ^6.5 || ^7, a version of phpspec/prophecy that matches ^1.7, and a version of symfony/phpunit-bridge that matches ^3.4.3.
Even with Drupal 8.8.0, installing PHPUnit after installing Drupal core with drupal/recommended-project requires the same steps I described for Drupal 9.