Start with importance
The single biggest lever is notification importance. In Settings → Notifications → [app] you can set a channel to make sound and pop on screen, or drop it to silent. Move the apps you care about to the top level and push the noisy ones down. Visibility starts with what is allowed to interrupt you.
Give key apps a distinct sound
A unique ringtone or alert tone for messages, calendar, or your baby monitor means you recognize what arrived without looking. Generic pings all sound the same and get ignored. Set a short, distinct tone per critical app.
Use color and lights
Some phones show a colored edge light or an app icon badge for new alerts. On supported devices (including many Samsung and Xiaomi phones) enable the notification light or edge lighting for priority apps so a glance at the phone tells you what is waiting.
Show on the lock screen
Make sure important apps are allowed to show on the lock screen (Settings → Notifications → lock screen). You will see the alert without unlocking. For privacy you can show the app name without the content.
Keep the critical few on top
Even with good settings, a busy shade buries things. For the alerts you absolutely must see — a code, an address, a reminder — pin them with Dingpin so they stay at the top, color-coded and impossible to miss.