Health check is a broad topic. It all depends upon your server role. If server is a load balancer than; I'd monitor LB software and network closely apart from system load. Try
- Logwatch - Watch your logs in /var/log/* for errors, security and warnings and sends daily email summery report about them.
- Nagios - a popular system and network monitoring software application. It watches hosts and services, alerting users when things go wrong and again when they get better including cpu, memory, network, log files, disks, MS-Windows clients, server temperature & over all health and tons of other things.
- sar - It collects, report, or save system activity information last 30 days or so. It can answer why load was high at certain time of the day.
- There are many other software and plugins to monitor specific part of the system. If you need any specific info let us know.