Woohoo! Welcome to the club 
A lot of what I’ll say seems to become more critical the longer you go (for example you might be able to run a mile in lousy shoes without getting a blister) but I think it’s good to develop the right habits early on so here goes.
Blisters. The right socks (something other than cotton) and good, proper-fitting running shoes will make a world of difference. Keep calluses under control (a blister under a callus really sucks).
Chafing. Can happen pretty much anywhere your clothes touch your skin. Make sure that clothes fit properly (i.e. your shorts aren’t too tight) and wear wicking materials. Again, no cotton (it gets wet, doesn’t dry out and sticks to your skin when wet, a horrible combination. It’s also a crappy insulator). There are friction-reducing substances including Gold Bond powder, Blister Shield foot powder, Body Glide and others that can help with trouble spots.
Runner’s toe. General toenail problems like black toe, losing toenails and so on (that sounds like some kind of hideous torture but it’s not really painful, just gross). Keep your nails properly trimmed and smooth (so they don’t catch on your socks). Make sure your shoes are the right size so your toes don’t keep bumping into the toebox. This seems to be more of an issue if you do a lot of downhills since that’s when your foot slides forward in the shoe.
General sprains and strains. There’s a ton of different muscles and joints and parts that you’re exerting, certainly everything from your toes up to your lower back. Don’t push yourself too hard too fast, go at a comfortable speed (if you can keep talking or mumble along with your iPod you’re at a good pace) and increase distances slowly (I’ve read 10% per week is good assuming that everything else feels fine). Especially when you’re just starting it’s easy to overuse something and get a strained muscle, sore shin, random foot pain and the like. Go at your own pace and really listen to your body; you’ll learn the difference between “X is sore” and “X is injured” but play it safe, if something hurts, stop and take care of it. Careful stretching, RICE, and other topical measures are good. I used to be one of those “I’ll work through the pain” guys and on a few occasions I aggravated a problem which resulted in longer layoffs than if I’d just rested the thing and let it heal to begin with.
Stay hydrated and protect yourself from the sun & heat.
Do some general strength training, remembering to include your core (abs/back) along with the rest of your upper body as well as your legs. There’s plenty of simple exercises you can do at home with little to no equipment and that don’t take much time. If you are stronger you are less likely to get injured.
A couple of books that I have found handy include Jeff Galloway’s “Book On Running” and John Vonhof’s “Fixing Your Feet”. The former is great when you are starting out. Galloway is big on mixing running with regular walk breaks to prevent injury - I use this on my long distance runs and it works well for me. Vonhof’s book is all about prevention and care and it’s aimed at endurance athletes but I think it’s very valuable - avoiding blisters is just as critical when you’re starting out as when you’re running 100 miles.