re: new note 3

When you unlock your screen and look at the screen, or swipe to another screen, that is your launcher. Basically your home screen(s). You are currently using the touchwiz launcher, but there are a ton of other launchers out there that you can use instead. In most people's opinion (mine included) nova launcher is the best. It works the same as your current launcher, but it allows you to customize most stuff on your screen. Want more rows or columns, or want to make your app icons smaller or bigger? You can adjust widget sizes, create gestures (like a swipe up will open a certain apps). One of the biggest thing is icon packs. With a different launcher, you can customize what all of your icons look like with icon packs.

Nova now has hotword detection, so you can just say "ok google" to open up google search.

Pocketcasts is a great app for podcasts, if that's your thing.

Also, don't forget to download Google Opinion Rewards. Every once in a while, you will get surveys from google, and when you complete them, google will give you google play credit. I used to get them all the time, but it has slowed down a bit.

If you are on ATT, get their Visual Voicemail app. It will make your voicemails like the iPhone voicemails.

I don't really have any Note 3 centric apps that are a must have. I rarely use the s pen, so maybe somebody that uses it more can help you out with that.