Are non 'copy-only' full backups safe to recover from?
However, there is no need to do point in time restore on any of them at this point.


If this is the case you MUST put database in simple recovery mode and this will take care of the transaction logs. When database is in simple recovery mode you can take two types of backup
1. Full
2. Differential

Depending on how much data you can loose you can take daily full backup and then may be differential backup twice or 4 times a day just to make sure you loose as less data as possible. When you restore from backup you would have to restore the latest full backup and the latest differential backup taken after the latest full backup. You cannot take transaction log backup in simple recovery model SQL Server will itself manage your transaction log truncation. 

Please read Understanding Logging and Recovery in SQL Server


  Am I right in thinking that a database can be restored from a full-backup at the time that full-backup was taken


Yes you are absolutely correct. Please read Understanding Backups in SQL Server