At this point, Android's notification system is pretty elegant. But there's no way to avoid confusion (and for some users, frustration) when a ton of notifications come in all at once. Echo Lockscreen attempts to fix that with a lockscreen replacement that puts your current notifications front and center, then organizes them by app or urgency. Currently Echo is in alpha testing, and it's a free download in the Play Store.
When it comes to getting various notifications while your device's display is off, a built-in LED is useful. However, it's far from perfect. Sure, you can customize each notification with something like Light Flow, but that doesn't let you know the message contents at a glance. And, of course, there are also devices that don't have an LED at all, like the Nexus 7 for example. If you're looking for more out of your notification experience, Knock²+ may be the answer.