My iCloud storage is full and I would like to delete my back up on my phone. I want to continue to back up my phone with iCloud. should I just purchase more iCloud storage or will deleting this current back up free more space for future back ups?

Deleting you current backup will serve no useful purpose - as it will be replaced when the next backup cycle occurs. However, as iCloud backup is incremental, the next backup will take considerably longer than normal - as a full backup will occur instead of an incremental update to an existing backup.

Also consider that if something were to go wrong, there will be a period of time for which you don’t have a backup from which to restore.

If your iCloud storage is full - and you have no other file-content or Photos that you are prepared to delete, you ought to consider subscribing to a higher tier of iCloud+ storage.

Upgrade to iCloud+ - Apple Support

iCloud+ plans and pricing - Apple Support