The original model is the one with the memory card slots on the front (and the only one that comes in white). The S came out in ~2010 has an angled, thinner-in-the-middle design, and the E (came out when the Xbox One was announced) looks like a smaller Xbox One with rounded corners.

The problems I mentioned weren't universal, but they were about as close to it as you could be. Maybe you had an S or an original model that was later in its production.

The 360 has a one year general warranty, but the red ring problems were so widespread that Microsoft added a three year warranty for red rings specifically.