I am planning on buying an Xbox but am confused by all the different versions. What are the differences between them?
The Xbox 360 hardware has gone through 3 major revisions:
Here's a photo from a CNet review of the E:
The one on the left is the "old style" Xbox 360. There were a couple of versions of this, and some early models did not come with HDMI ports. You're only going to buy one of these if you buy used, and I'd be careful. A lot of the early run had issues with overheating and were prone to the "red ring of death."
The middle unit is the Xbox 360 S. It improves on the classic 360 by adding a dedicated Kinect port, additional USB ports, integrated wireless and a built-in optical audio out. All of these models come with HDMI ports.
The one on the right is the Xbox 360 E. It is a redesign of the 360 S to make it look a bit more like the Xbox One. However, they dropped the optical out, the AV port (for Component video) and a USB port. There's no real advantage to this model as far as I can see. (The linked CNet review says the pros are it's "slightly quieter")
In addition to these models, there are also variants of each of these. Usually it amounts to a difference in the amount of storage. There are also various bundles that pack in games or peripherals like Kinect.
It seems clear that for almost any way you could judge the three, the Xbox 360 S is the winner. The only advantages the E has is similarity in design to the Xbox One, and perhaps a slight noise difference. The "classic" 360 is probably cheaper, but buying one used is slightly risky.
There's some more detail and a somewhat-useful table in this Wikipedia article.
Aside from appearances, the most significant differences between an original 360 (2005-2008) and the "S" / slim version (2010) are related to the processor type, power consumption, and heat dissipation, all of which significantly affect the long-term functionality of the system.
From the table below (source), we can see that the Valhalla processor used in the Xbox 360S is the most power-efficient and therefore has the least amount of system heat. The best possible processor for the regular 360 is the Jasper; any processor revision prior to that will have higher chances of failure due to overheating.
Also, the 360S has a more sensible ventilation design where the grill is on the top of the system (vs. the back of the system like in the original 2005 design), allowing heat to dissipate naturally upwards.
I got an original No-HDMI out Xenon model from a friend for precisely the price it's worth.
That's the only way anyone should bring one home.
One way to spot the Jaspers is by looking at the label on the back. If your looking at one of the original chassis, you do NOT want one that says 12V 16.5A or 198 W. Again, unless it's free. I'd honestly recommend never buying one from EBay or Craigslist at any price, since you don't even know if the insides match the label.
From Gamestop, might be worth it on a refurb since if it's a Jasper (12V 12.1A or 145.2 W) according to the label, it almost certainly really is one. However, I'm seeing refurb bundles on the classic chassis for only 10-20 bucks cheaper than a refurb bundle on a similar S or E.
Take the S, or the E in a pinch.
I only even took the original non-HDMI Xenon for free as a Windows Media Extender point for a 20" tv I don't care about HDMI on. When it dies, it dies.