You may want to take care of that plantar fasciitis before you start running. Running is really hard on a person's body. so, if you already have an injury and start running, you risk making that injury worse than it already is.
I've had PF in past. It took me months of not running to get my feet to heal. You may want to consider other activities that are less high impact. Have you thought about cycling ? riding a bike is wonderful cardiovascular exercise. Swimming is too. Many injured runners start swimming when they can't run because of an injury. You don't have to run to be fit and lose weight. When it comes to weight loss, what matters most is what we eat. Good nutrition is what takes the weight off and keeps it off. Exercise is what keeps our bodies fit and healthy.
For now, instead of running, why not walk or ride a bike ? give your feet time to heal before you decide to run. If you do want to start running, then consider a couch to 5K program. A C25K assumes no prior running experience and will literally take you from your couch to a 5K road race.
Also, if you do decide to run with the PF, which I don't recommend, then you really need to be fitted for a GOOD pair of running shoes. Wearing ill fitting running shoes will also cause futher injury. So, if you're going to run, make sure you're wearing a proper pair of running shoes fitted by a reputable running or sports store. www.sparkpeople.com/resource/fitness_artic
How about walking a 5K instead of running ? It would be a lot less wear and tear on your feet.