Is Nagios the right tool for this job? And which version?

Nagios
1

Hi I

2

Yes, nagios can monitor that stuff. I use the check_oracle plugin to monitor all the freespace in the tablespaces, connectivity, oracle instances, etc.
If you follow the docs to the letter from A to B, you will have at least one host being checked in 2 hours.

I personally will not use any nagios version over 1.x. If you do go above, you will have a few little things to deal with.