On the championship courses I haven't seen a walker in the four years I've been here. On the executives, my neighbor and I play them a few times in the winter when the green fees are higher on the championship courses and we both walk. I'd say about a 1/3 of the golfers on the execs walk, maybe less on some of the harder ones like Pelican. By walking you pay absolutely nothing on the execs, the normal $4 fee is for using your cart, so that is eliminated.
The main reason we walk on the executives is because if you ride, it's only about 90 minutes to play 9 holes. To me, it feels like I haven't even broken a sweat or done anything. By walking we at least feel a little exhausted. I use a Clickgear 3.0 push cart, it's one of the most popular and sells for about $200. That way I can use the same bag and don't have to swap anything out between 2 bags. My neighbor uses a small carry type bag that you have to lay down. If I was buying a bag for walking, I would get a stand bag, which has pop-out legs. They stay upright when you sit the bag down next to your ball and is tilted at a good angle to pull your club out, they are also on the lighter side and sell for $50 to $100 on average.