I want to create logging/console utility accesible from web, where I can check in realtime some basic status of domains, see last PHP and Apache errors and warning messages and so on.
My question, aside from implementation of above features, is how to store that log data, and how to pull it from server with minimum traffic.
Your requirements seem to have a perfect fit in HTTP Push technologies. If you are in control of the client (i.e. you know it will be a modern, standard-compliant browser) you can use the offical W3C EventSource or WebSockets. Otherwise, you’d have to poll at regular intervals using AJAX or just refresh every 15 seconds.
About the storage itself, the cleanest solution would be if you directly store your logs in MySQL (Apache guide). If you feel inspired to try something new, you could experiment with NoSQL databases, but I don’t have much experience there.