Please help me

I don't understand any of this at all. I'm not going to get into the start of all this, but essentially I just need to backup my iPhone now and have never done so before. I'm using a 5s that I've had for about two years and just want a simple and easy way to back up all of my data so I don't lose it. I have three apple devices, all of which I struggle with and can rarely find any helpful advice (if you can't already tell I'm not at all tech-savvy), so I'm hoping making an account here will actually bring me some answers.

I was told iCloud was the easiest option and reluctantly tried it. Immediately an email was created for me and then it said I didn't have enough storage to back up my data, as there are only 5GB of free storage. Not willing to buy more storage, I decided to plug it into my Mac. This I didn't want to do because I synced my iPod to my Mac, which for reasons unknown was unable to hold all my music (claiming not enough storage when there was and still is plenty), meaning some of my music is on my Mac, while most is on my old PC, so I can't use my Mac to sync my music without losing most of it. Additionally, my iPhone automatically synced wirelessly with my iTunes account (something I found very annoying), meaning every now and again, some music randomly ends up on my iPhone if I have wifi. Completely unwanted and irritating, but anyway I plug my iPhone in and automatically it starts syncing with my iTunes on my Mac, downloading some of my apps (claiming there to be 30, but only 8 are present), mixing this weird mashup of music I don't want on either device and freezing my mac for a while, as I scour the internet for solutions. It then says there is not enough storage to back up my device, even though there should be, but there is no way for me to manually decide what I want to be backed up and what I don't, or at least none that I can find.

I then realise iTunes doesn't seem to be backing up my notes and pictures (which are the most important things for me to back up), so I go back to my phone to see it's giving me notifications about iCloud storage memory. I try to delete the iCloud account, which gives me a notification saying if I do so, all backed up data will be deleted from my phone. I then try to un-sync certain apps with the iCloud, where I get the same message threatening to delete it from my phone. So it seems I'm stuck with the bloody iCloud, which means whatever's been partially backed up there can't be backed up to my iTunes, the back up for which was likewise only partial, with no information on either platform about what exactly was backed up, yet both record a successful back up despite me receiving the same message from both there was wasn't enough space. I know I sound like an idiot, but I am losing my mind over this simple problem there seems to be no solution to and everywhere I go I get unhelpful or generic advice, get sent to an equally unhelpful FAQ page, or redirected to an apple help page that no longer exists…

I just want to back my data up (and preferably learn how to get rid of the iCloud account without losing data, remove all the data on the iTunes on my Mac without losing it on my other devices and get rid of all the unwanted music on my iPhone), I'm also not willing to pay for more storage, because that is ridiculous and I'm not paying for an untrustworthy system that I'm still not sure who it will make my personal data readily available to. I really just want a place to back up and save my data (my notes and photos in particular) and I'm pulling my hair out because I don't understand any of these new apple systems that automatically do everything I don't want them to do.