I'd suggest finding a team that can evaluate the website to tell you how to minimize or eliminate the worry of downtime. If the tech stack is good and maintained any downtime will be the responsibility of the hosting company.As a Professional Services company, we often have to tell folks that even if we did 24/7 support for you we could do nothing if the website goes down. We've got the tech infrastructure in great shape and up to speed so if the site goes down the host has to be the one to fix it, and they monitor that in their house, if it's a host worth having. All we'd be doing is calling the host to say 'hey the site is down' and they'd reply 'we know we're working on it, please view our status page for updates' and then we'd ferry that message.Getting the bones right and put on the right hosting for your needs is what's going to keep your uptime minimal :)
Any specific suggestions would depend on the core code your running.
When I worked for a SAAS shop we had ur host restart servers that went down, but we paid for premium hosting from a buisness-class host (Peak 10).
We used New Relic for monitoring because it could monitor and give us history on individual modules and tell us, for example, if we had a memory leak.
I don't think any of that is going to come cheap.