I have an external monitor with a VGA connection. What is the best adapter to use for my Retina MacBook Pro? I think I've seen Thunderbolt to VGA, or USB to VGA? Or HDMI to VGA? What are the differences?
You should get a mini DisplayPort to VGA adapter (sometimes referred to as a Thunderbolt to VGA adapter, but it's the same thing). Apple sells one, but they can be had elsewhere for less, including at my personal favourite, Monoprice.
You could do HDMI to VGA, but it would require a (typically bulky) active adapter. There are some HDMI to VGA adapters that aren't active, but they rely on graphics card support that Macs don't have. The DisplayPort to VGA adapters are technically active adapters, but for whatever reason they seem to be much more compact than HDMI to VGA ones.
There are USB based display adapters, and some of them have VGA output, but I'd only recommend them for situations where other outputs aren't available. They're essentially a USB connected graphics card, which means that performance is lacking, and it takes up CPU and memory resources that the built-in outputs don't. Useful for some situations, but in your case I'd stay away.
Clarification: I have a thunderbolt of mini display to VGA cable, which I had been using to connect an LCD with my old Mac Pro Book for over 4 years. Just bought Retina Mac Pro and when I connect to LCD through this cable only the screen background appears on the LCD display screen. All efforts failed so far to get the word or ppt files or another display from the Retina Mac Pro to LCD screen.
It appears to be a serious issue and probably calls for the attention of Apple Service people.
Having your background only displayed is an entirely different (and much easier) issue to solve. What's happening is that one of your primary (selected) desktop is being shown on the Macbook's display and one of your other Desktops is shown on the projector.
You've got (at least) two ways to deal with this. 1) Look at the very top of your Macbook display - up in the top, right hand corner. You'll see the searchlight magnifying glass, to the left of that you'll see your user name, the time, date and day are to the left of that, the battery indicator to the left of that, then the speaker symbol. Next you'll find the display preferences. If you're connected to another source (a second monitor, a projector, etc) you should have choices - "Mirror Retina Display" will "project" the same thing that's showing on your Macbook. "Use as separate display" actually extends your display space so you'll need to grab whatever it is that you want projected and drag it into the extended display space.
If you're using the projector as a "separate display space" you can also open the display perferances under that same icon which will let you modify the logical position of the displays making the extended space above, below, to the lef, or to the right of your Retina display. It's less complicated than it sounds. I hope this helps.