Hi Jelepilly and welcome to Android Forums!
The apps I cannot live without:
Cerberus anti-theft
AVG anti-virus/malware
Camscanner scan/fax documents
Chrome Beta, my browser of choice
Robin a great assistant
Gas Buddy helps you find the cheapest gas around
Quickoffice is a Office editor for documents, spreadsheets and presentations
Google Keep an awesome to-do organizer
Chrome-to-Phone for sending stuff from your PC to the phone
CameraZoom FX and HDR+ are awesome camera apps
Soundhound for identifying songs: even produces lyrics!
SwiftKey Keyboard the best keyboard for Android
Tune-In Radio for great streaming FM radio stations all over the place
Thunderstorm Live Wallpaper - drop dead gorgeous on this screen!
Someone else will help you with Themes, as I prefer my phone pretty much stock Android. Hope this helps.
It's great to have you here and enjoy your Note 3!