We always stay IN the park for the best experience.
The comments that West Yellowstone is "walking distance to the park entrance" and "the park entrance is a few minutes away" are misleading.
If you're going in the summer, you're going to have a line of slow-moving cars before you even get to the park entrance gate. Then you'll have slow-moving vehicles until you get to Madison Junction and all other areas of the park. Old Faithful area is a nightmare but you've got to do it. :) Also, if you "walk to the gate", you'll have many miles of walking and days to do it in order explore the park. Yellowstone is not a walking park.
If you need full hookups I would highly suggest staying IN the park at Fishing Bridge RV. A good easy way to see the park if you're planning on five or more days, is to move within the park to different campgrounds. If you need a shopping fix then take a half day and just drive over to West Yellowstone.
Also, it's recommend that you don't try to 'do' the adjoining Grand Teton Nat'l Park from a spot near Yellowstone. You could never do it justice by doing that in a day. Instead, move down to the Tetons and enjoy it's beauty for a few days. It's altogether different from Yellowstone.
Enjoy your trip!