If this is fixed to only one customer then Solarwinds perhaps. If you want to extend to other customers then you might want a true multi tenanted tool.
We have used Nimsoft of old, but growing issues with the product changes have reduced its reliability and usability for us to a point where its a bigger risk than a benefit so we are moving away from it.
We have recently moved to Sciencelogic, not free but very capable with a large number of automation actions built in. It seems clean, agentless, reliable and quick so far in the POC we ran and now the initial install and migration of our customers.
Although I have limited knowledge of it, it sounds like Nagios may be closer to what you want if a free solution.
Mileage will always vary depending on your in house skills and time availability for management and customisation. If you want to utilise contractors occasionally for complex elements at short notice, it is worth scoping out what skilled resources there are out there for your software of choice, and what support is available if you REALLY need it. Free is okay, but is a risk if you are charging your customers for a service that the software underpins.
You tend to find using a monitoring tool is just the start of the 'art of the possible'. Its rare you will stick with a pre set scope of parameters, especially where customers dangle money as an incentive.