I'll be in Yellowstone for the first week in October. From 13 years of experince in the park at this time of year, I recommend that you prepare for extremely cold and wet (snow and rain) weather. You might, of course, experience an Indian summer, but it's quite likely you will experience some heavy weather.
Try to make it to Lamar Valley a little before dawn - look for parked vehicles, and people standing around w/ spottings scopes and radios. These are the wolf watchers (you'll become one, too). Radio communication along the road means if wolves are spotted, everyone will be able to drive to the location to view them. Will you see them? Autumn is the worst time to see them, but there's a good chance you will. Can you photograph them? Usually too far off, but it's an amazing experience.
Hmmmm....Lamar Valley is a long way from W. Yellowstone to make it by dawn. I'd consider spending a night in Gardiner, just n. of the park. Lots of inexpensive motels to choose from. It's about an hour from Gardiner to the Lamar Valley.
Can you hike (probably not with all that camera gear!). Park at the Grand Prismatic Pool, walk across the road, and look for the steep trail leading up the hill in front of you, leadind toward your right. It takes about ten minutes for a fit person with a moderately heavy camera bag to make it to the top. There's an awesome view of the pool from here.
Keep in mind that when it's cold, there's usually too much steam from the geysers to photograph anything but the steam. If it's warm, there is no steam. Temps in the 50s-60s seem to be ideal; you want some steam, but you want to see some color in the water, too.
As for geysers, I really like Castle Geyser, near Old Faithful. It goes off every 11.5 hours or so. Try to find out the predicted time, if you are there, it goes off for about 40 minutes, with a lot of roaring. Often, depending on where you stand, there's a rainbow in the spray. (Wipe any spray off your camera lens, a chemical preciptate, sinter, can damage your lens).
I like to wake early when I stay in the Upper Geyser Basin, near Old Faithful - I walk out to the bridge that's beyond Castle Geyser, and photograph dawn over the Firehole River. In the early a.m., there's a lot of steam when it's cold, and the scene is unreal. As the morning warms - if it does warm - the steam dissipates.
Keep back from wildlife. If the visitor center is open at the Canyon junction, look for the looped tape at the buffalo (bison) exhibit - there are scenes of people being gored/trampled/tossed into trees by the bison because they got too close.
Buffalo? - Usually in Hayden Valley. Elk? Mammoth Hot Springs - where you will want to take the little side trail to Canary Springs. However, the trails shifts because the springs shift over time.
Ice cream? Try the general store at Mammoth.
T-shirts? Lots of them in W. Yellowstone, many of them with wilder and crazier artwork than you'll find in the park. Go into Gardiner, just past the north entrance to the park.
And while you're headed into Gardiner, watch the cliffs, particularly on the east side of the road, for Bighorn sheep, and antelope on the flats near the park exit.