Most walkers who cover long distances seem to prefer running shoes, as they are more flexible and have more padding. It's mostly a matter of preference. What's important to remember is that the shoe should fit well and give proper support. You don't need any special equipment, except for a good pair of shoes. If weather is a problem, visit a local mall.
Many malls open their doors early to allow people to walk inside.
There are several Internet sites that list upcoming races with contact info. If you are in California, RacePlace is a good one. ActiveUSA is another, which allows you to search various states and types of events. They also have a good walking section, with message boards, tips, and training tools. Remember, many events may not advertise that they are open to walkers, but most races will allow walkers.