Logs of your online activity---web history, search queries, purchases, etc---are the most concerning. These can be used to directly spy on you, and any VPN that engages in this sort of logging should be avoided at all costs.
The second priority are identifying metadata logs. These include information that can be used to identify you and corroborate online activities. Your IP address, the IP address of servers you connect to, and connection timestamps all fall into this category.
Lastly, there's diagnostic logs. These are not much of a concern because they cannot be used to track you or your activity. Dates (not times) connected, the last location you connected to, and amount of data transferred are not privacy concerns for the vast majority of users.