What is the easiest way to set up an SMS alerting system so that I will receive notification if my server doesn't respond or a GET query doesn't return correct content?
You can completely outsource the monitoring and alerting, for example by subscribing to Pingdom. The most basic Pingdom plan will monitor up to 5 services (including using HTTP GETs with optional content pattern matching) and send an SMS after a configurable amount of downtime.
If you want to roll your own solution, the first thing to get right is the monitoring software. Many, many third party solutions exist for this, from the free to the outrageously expensive. Of course, rolling your own "try a GET and do something if it doesn't work" script is always an option, but as with all software, feature creep may mean that you're just re-implementing existing solutions soon...
For the SMS notification, using an e-mail-to-SMS gateway might work for you, if you're in a territory well-served by such services. Most US providers, for example, provide free gateways, whereas in Europe they tend to be run by third parties and pay-only. As already suggested, Google is your friend here. Also, your monitoring tool may support sending notifications directly using a cellphone/GSM modem attached to the monitoring server.