Disclaimer: Advice is provided to the best of my knowledge but no implicit or explicit warranties are provided. Since the advisor explicitly encourages testing any and all suggestions on a test non-production environment advisor should not held liable or responsible for any actions taken based on the given advice.
As our friend told you have Oracle Enterprise Manager dbconsole to monitor all stuffs
But as a growing DBA you can write your own monitoring script by using Perl/sh or any scripting lang for gaining indepth knowledge.
I can help with few things.
1) Tablespace growth check, if the space reaches limit automatically increase size
2) Database instance connectivity check
3) ORA error message check in alert log file.
4) Tablespace online and offline check.
5) Any session holding locks for 30 mins.
6) Montior trace file ans remove it older than 7 days.
7) Space availabilty for next backup.
8) Monitor Temp tablespace usage.
9) Backup related script.
10)Database statistics from statspack.
11) Start and stop all DB servers.
12) etc,etc ................