What is a tower case and is it right for me?

A tower case is this size of case. It is a good value choice for compact builds.

Will my graphics card and cooler fit a tower case?

Check three clearances: graphics card length (high-end cards can be over 300mm), CPU air cooler height, and radiator support for an AIO. Most parts fit comfortably, but it is still worth checking the maximums.

Does a tower case have good airflow?

Airflow depends on the design more than the size, so look for a mesh front panel and room for several fans. Many cases pair a mesh intake with a glass side panel for both cooling and looks.