Hi renegade,
To answer your questions, meditation using mantas has been around for thousands of years. I do meditation for anxiety, but it can help with depression also. The reason that I tried it, and I'm glad I did, was because I read a book by a Japanese psychiatrist that taught people with anxiety disorders Zazen mediation to calm them down. He discusses how meditation will produce alpha brain waves in experienced meditators. He also mentions that mantra meditation will produce these alpha brain waves. He used an EEG to record the brain waves. Alpha brain waves occur when people are relaxed, and are most prevalent just before you enter sleep, as you start to drift off.
Mantra meditation is much easier to learn and will cause these benefits very quickly, while Zazen meditation is more difficult and it takes a while before you acheive much success.
It is not so much a distraction, it gives the left side of the brain something to do while activating the right side also. Most activities just envolve one lobe of the brain, this involves more. I don't know all the ins and outs, but this form of meditation has been studied the most and it has been shown to reduce stress, reduce stress hormones, and help with depression, anxiety and drug dependance.
I recommend picking a short mantra. Find one you like, and stick with it. Don't keep switching mantras. By the way, let your head hang down, let it all hang out, so to speak. I often fall asleep, and wake up feeling very refreshed. I think of it as 'power napping'. I could go on, but i don't want to bore you. By the way, I spent $500 to learn this method (which i gave you all for free), but i still consider it worth every penny, it really has helped me during some stressful times.