For visual astronomy aiming to see faint nebulas, what single piece of equipment is most important for detecting dimmer objects?

The aperture of the telescope, as its diameter directly correlates with photon collection ability.

When the goal is the visual detection of inherently faint objects like nebulae, the single most critical factor related to the equipment is the aperture of the telescope. Aperture is defined as the diameter of the primary light-gathering component, whether it is a mirror or a lens. This physical dimension determines the total number of photons that can be collected from the distant object. Increasing the aperture effectively boosts the apparent surface brightness of the target object relative to the background sky darkness. While eyepieces affect magnification and filters can influence contrast, neither can substitute for a lack of initial light collection; using excessive magnification on a small aperture telescope will dim the image to the point where the already faint nebula vanishes completely.