The most important piece of gear to bring is your open and inquisitive mind.
Sturdy walking shoes with non-slip or high traction soles, a good hat/cap, and layered clothes for varying temperatures and moisture conditions are essential.
The best camera to bring is your favorite camera, the one you’re most comfortable with. This could be a film or D-SLR, a mirrorless, or a cell phone camera.
Given we’ll be inside the barns for some of the photos, in low light, a tripod will be most helpful.
If your camera has interchangeable lenses, the most useful are likely to be a telephoto lens from 20mm to about 80mm, and also a macro lens for real close-ups of barn implements, flowers and insects. Most cell phones have a choice of lenses.
The most useful filters are polarizing filters and graduated neutral density filters for landscape views (but I generally use Lightroom and Photoshop for post-processing instead of these filters).