I just recently downloaded the Android SDK.
Downloading all the packages in the "SDK Manager" will take way too much time. So I'm wondering whether I should deselect all the platforms except the latest one.
Do I need all the platforms or which ones do I need?
Not at all. You just need to install those platforms which you are targeting for your apps and which you intend to test your app with. If I were you, I'd install:
You should also install
Optional: