I'm worried I might log in one day and my fully configured instance has been removed. I would like to be able to back it up daily to S3 but frustratingly this is not a simple setting in the console.
Is there a simple managed solution that can take care of backups, and should the unthinkable happen, allow me to simple restore it straight away?
I'd like to recommend my open source tool "ec2-automate-backup" in combination - the tool will snapshot one or more than one EBS volumes - your server (or servers) can then be restored from these snapshots - the tool is available at http://awsmissingtools.com
Best way is to use an EBS backed instance - you'll pay a little extra for the EBS storage, but it's worth it for the peace of mind. Use one of the available EBS backed AMIs, or follow this Server Fault answer to roll your own from a running instance.
You can use EBS volumes for your data and keep it snapshot daily/hourly using cron job.
Once you created a snapshot, you can create a new volume from that and attached to your new instance(create with same AMI you have). You can also automate your AMI, where you can pass a user-data(ex. volume-id) upon startup for example, which will auto attached the volume and snapshot it.