For backpacks we use the Golite Rush. Love it and I run in it daily with no signs of wear after a year of use and many washings.
Bikes - As someone said, the light the better but you can use anything you want and many of the sport teams run Walmart level bikes. You would want to upgrade from those if you decide the sport is for you. Check Craigslist, there are some great deals there. I ride a Motobecane Fantom Pro Ti from Bikesdirect.com. I love the Motobecanes and think they are the best bang for the buck in a hardtail bike. I also recently added a Thudbuster seat post to my bike and it's saving me some rear end soreness over long rides.
Bring a change of socks/shoes and plenty of food and water. Train with the food that you want to use during the race. I use Clif bars, my wife is gluten-free and uses Lara bars.
Compass - The Walmart level compasses are probably fine for a beginner, but I bought a higher level compass for its accuracy and responsiveness and like it a little better. The link recommended above is mandatory reading as to how to use the compass. You might also hit up some local orienteering events to get some practice.
I highly recommend avoiding any cotton clothing at all. Instead, choose wicking clothes and socks, and use Bodyglide on your feet if nothing else to help prevent blisters. You will most certainly get wet and dirty!