Upgrading to a new iPhone - what do I need to be aware of?

My four year old phone works for about 15 minutes before requiring a recharge, meaning that it's effective an im-mobile phone. I'm going to get a new one but before I do I need to back everything up or it will be lost forever.

I'm not the most confident backer-upper of phones and for most of its life I've never let it anywhere near a computer (for fear that iTunes will launch and I'll never hear the end of it). My phone's capacity is 32GB but I have a little over 16GB on there. A couple of weeks ago in preparation I did let it do its thing with iTunes (it was a little like the priori incantatem from Harry Potter - nothing good has ever come of letting iTunes and my phone talk to each other). It may or may not have backed itself up, it says it has but I've no real way of knowing. Or of understanding it.

What do I need to double check, and how do I do that? Here are some 'genres' that I've thought of but if you think I've missed anything please suggest in the comments or tweet me @JoBrodie (or email's above).

• Email - I use IMAP so I assume that when I get a new phone I just whiz in my login / password details and it will download everything from scratch
• Music - I think this is what iTunes has done, all the stuff I've bought directly onto my phone (pretty much everything) now seems to be saved on iTunes
• Photos - best decision I ever made was to say 'yes' to Dropbox when it asked me if I wanted to sync my photos to Dropbox and earn an extra umpteen gigabytes. Every time I connect my phone to my work computer (which doesn't have iTunes on it!) my latest photos synchronise and save to Dropbox, so no worries there
• Notes - I'd hate to lose these. I could email them all to myself, or copy and paste the text into one massive note and email that ;) Is there a simpler way?
• Sound recordings - via the little microphone app that is part of the iPhone. Again I can email them to myself but is it possible to back up more efficiently.
• In-app settings - I've loads of apps, some much used, some less so - will I be starting from scratch and having to download them all (I have a list from all the iTunes receipts sent to my email address). I also have some sound recordings in another app - would hate to lose those. Also I have apps that have recorded walks I've done in London. Some I've managed to upload some not and I'd like to know I can still access these when I get a new phone.
• Calendar - I was a bit sad when I left Diabetes UK and lost access to that email account to suddenly lose years' worth of calendar entries which I'd foolishly tethered. Just whoomphed out of my phone in one fell swoop. How can I better protect my calendar?

Backing up to the cloud - I used to do this until it told me I'd exceeded my limit, so I switched it off (otherwise I'd have had to buy more storage space). Can I clone a 'disk image' of my iPhone on my Mac? I've no idea what that might entail but I've heard people talk about disk images so I thought I'd throw that out there.

A few weeks ago I tried to buy a new iPhone believing that Apple would magically whoosh the contents of my phone onto their magic cloud server, sell me a new phone and then whoosh all the data onto it. I was a bit surprised and disappointed to have the rude awakening. To be fair the assistant was extremely helpful and explained how to do a back up (and also the online help pages are pretty good) but I do think that having more intuitive software (looking at you, iTunes) would be more in keeping with a company that has this amazing hardware.

I'll be sorry to say goodbye to my old phone when I move to the next one, but I'd be sorrier to say goodbye to all my useful stuff.

What did you wish you'd known before you bought a new iPhone?