Q: Problems restoring 5c 32gb to 6s 16gb

Hey Stressed Mum,

I can understand your frustration with trying to fit everything on your previous phone to your new iPhone 6s. Let's see what can be done so you can be up and running. 

The first thing I would look at is your iPhone 5c. What you will want to do is enable iCloud Photo Library as this does not count towards your backup in iTunes or iCloud. This will upload your photos up to iCloud and keep all your devices synced together showing the same photos. Depending on how many photos you have, this can take up some time. Go to Settings > iCloud > Photos and enable iCloud Photo Library. You can also monitor the progress of uploading the photos. 

Once that is complete, you can make a backup of your iPhone 5c and restore it to your iPhone 6s. The steps for everything are in the next three articles. 

iCloud Photo Library FAQ
https://support.apple.com/en-us/HT204264

How to back up your devices using iCloud or iTunes
https://support.apple.com/en-us/HT203977

Restore your device from an iCloud or iTunes backup
https://support.apple.com/en-us/HT204184​

Now if you are still coming up short on space because the backup is to big, look at the usage of your iPhone. Go to Settings > General > Storage & iCloud Usage > Manage Storage to look at what could be taking up the space. You can ignore the Photos as those will be in iCloud and again does not go towards your backup. If you have a lot of messages with photos or videos in them, then that could be it. All you would need to do is remove those attachments or the conversations to reduce the size of the back up. Take a look at the link below to go over looking up your iPhone storage. 

Check your storage on your iPhone, iPad, and iPod touch
https://support.apple.com/en-us/HT201656

Manage your iCloud storage
https://support.apple.com/en-us/HT204247

Let me know if that helps.

Take it easy