Performing a backup with 24/7 availability
The missing piece of the puzzle is the overall size of the database. The larger the database, the longer it takes to back it up. While you may be able to afford some downtime, if your database is too large, your downtime window may be too small to perform a cold backup.
In either case, a hot or cold backup is still a good strategy. Hot backups require your database to be configured for Archive Log mode, but production databases should typically run in this configuration unless you have a good reason not to do so.
The next question to determine is how often to backup your database. If your database is small enough, you might want to back it up nightly. For a medium-sized database, you might want to perform weekly backups. Larger databases might be on a monthly backup schedule.
Another consideration is to use Oracle's Recovery Manager (RMAN). I highly recommend RMAN for all of your backup and recovery needs. The Oracle documentation has plenty of information on using RMAN. I also recommend the Oracle Backup & Recovery Handbook by Velpuri and Adkoli on Oracle Press.