I returned form Yellowstone last week. I planned this nearly 5 months in advance. We did speak with several people who were able to find accommodations for one or two nights, mid week, with little notice. We drove from Mt Rushmore to West Yellowstone. It is the best place to stay, if not staying in the park. When I do this trip again, I WILL stay in the park. From our site in West Yellowstone KOA, to the nearest point of interest in the park, was a 30 minute drive. Keep in mind, each subsequent day, the destinations get further away from the origin... The services in West Yellowstone were great. They had all the tourist stuff. I found decent prices on groceries and fuel.
4-5 days is probably what you will want to budget to get to most of the spots throughout the park. We did dinner at Old Faithful Inn, was great! We hiked to most of the "scenic overlooks" to escape the huge crowds that travel in large packs in the middle of the day. Some of the sights have horrible parking or access, we drove by and planned our return for later in the day when the crowds would be smaller. I also gauged the length of our stay based on the interest and energy level of my three kids. They each had their own interests and could only out up with so much driving, parking, hiking, watching steam... The info sessions, movies and exhibits at the various visitor centres are a great way to break up the day. There really is enough variety to cater to most people's wants.
In terms of what to bring, I would pack clothing for three seasons. We had everything from cold temps at higher elevations to impromptu rain/hail storms to 90+ degree heat. Lots of sunscreen is a must! While I found the flying pests to not be an issue at most places, as soon as you are off the beaten path, they find you. I was without bug repellant one day, not again after that though. Be prepared to stop and drive slowly through the park. You hear about it, and can see the videos pasted on Youtube. I can tell you, it is very real. People will park in the road, get out to take a picture.