Ok all this is hypothetical until you can actually connect to your production server to get the actual information and determine your requirements.
If your tapes can only hold 1 gb then what are you doing around your full db backup.
Your Tlog growth is dependent on the workload being undertaken. Once you understand the production usage then you can better determine your backup solution. To keep things simple and not knowing your system I would recommend the following as solution 1 - full db backup nightly with 4 hourly Tlog backups.
Your restore process is restore the full backup and all of the Tlog backups since your last full backup.
If you are concerned about the space usage then option 2 - full db backup on Sunday night, nightly differential, 4 hourly Tlog backup.
The easiest way to setup and schedule would be to create a maintenance plan. Ensure you select either the specific db or all user DBS. This will create a new file for each backup undertaken. You will need to setup a cleanup job to ensure you do not run out of space.