You need to free up space on the phone itself. Adding iCloud storage wont affect the phone itself.
Here are a few recommendations on where you can free up some space on the phone:
Uninstall iPhone apps you no longer need
Hold your finger down on the app for a few seconds until all the icons on your homescreen start jiggling around
Press the 'X' symbol in the top left hand corner of the app icon to remove it from your iPhone. (The app will still be linked to your iTunes account so you can download it again for free if you need to.)
Delete camera roll pictures and videos that you've backed up onto your PC
Click on the photos icon and then camera roll
Click on edit in the top right corner and then select all the photos and videos you want to delete.
Click Delete in the bottom right corner and then click Delete Selected to confirm.
Delete music and movies
If you have updated to iOS 5 on your iPhone, you can now delete music and videos from the phone without having to plug it into your PC.
Go to the music or videos icon and swipe your finger from left to right over the name of the Artist/Album/Track or Video that you want to delete.
Press the red delete button that appears.
Delete old Podcasts
The new Apple Podcasts App can start to take up a lot of space on the iPhone if it is set to automatically download your Podcasts rather than streaming them. You can delete the old information from the Settings menu on the iPhone
Go to Settings > General > Usage
You will see a list of all the Apps you have installed in size order. Find Podcasts in the list and click on it.
You will now see a list of all the podcasts you have downloaded on the iPhone. Click on the podcasts you want to remove and choose Delete to clear the information out.