Please look first on my explanation of Semver and this article about Semver in npm.
Patch updates are fixing bugs and security holes. They make your app more secure and stable, what you are hopefully want.
Minor updates are adding features. They don't change the behaviour of your app but make it future proof. They should not have negative side effects to you existing apps, but you need them to receive future patch updates.
Major updates are mostly big clean ups and redesigns. These updates include most times big performance and / or handling improvements and will mostly break your app. So it is a bad idea to upgrade the dependencies of your existing apps. But you can, if you want to use these improvements in your app (intensive tests and modifications will be necessary).
You should use the latest (stable) major versions if you are starting a new project to benefit from the latest improvements.