They are beautiful aren't they? Lol! One must have app is 'find iPhone' so you can see on a map where your phone is if you lose it and either lock, wipe it or send it a message so it can be returned. My DH and DD also have iPhones so we can use find iPhone to see exactly where we all are at any time. DD reckons it is a pain having to drop her phone off at school before she wags it lol.
I also love Shazam. It will tell you the name of any song you hear and if you want it will take you to it in iTunes so you can buy it.
'Tune in radio' will give you just about every radio station on the planet but it does chew up data.
A very handy one is iTorch. I use it all the time to find the front door key hole at night.
iBook is great for free or cheap books. It has a iPhone free user guide you can download.
There are great apps for kids. Have a browse in the app store.
And perservere with Siri. She is brilliant for reminders once you get the hang of her.