Should I make a taxonomy to organize data like this?

As I see it, since “incubators” is a way for you to group “startups”, “incubator” should be a taxonomy of a “startup” custom post type. Make sure, when you register your taxonomy, to specify the link between the two.

register_taxonomy( 'Incubator', array( 'startup' ), $args );

You can enter details to describe your incubator by entering data and having a custom template taxonomy-incubator.php (see the template hierarchy schema to understand which template gets loaded when).

Should you need to enter more info about an Incubator, there are plugins for that (if you only need a Taxonomy Image the WPCustom Category Image plugin is enough, otherwise look at WP Types or ACF).