Two to three inches is the number. Below that, weeds push straight through and the soil dries out by noon in July. Above four, water starts running off the top instead of soaking in, and the layer underneath stays wet enough to rot roots and grow fungus.
The most common mistake we find in Katy and Cypress beds is not depth, though, it is the volcano: mulch piled up against a trunk or a shrub stem. Bark is not built to sit wet. Keep the flare of the trunk visible and leave a few inches of clear ground all the way around it. A tree that has been mulch-volcanoed for years will have girdling roots to show for it.
The second most common problem is that nobody breaks up the old layer before adding new. Old mulch mats into a crust that sheds water like a roof, and dumping fresh material on top just makes the crust thicker. It needs turning or removing first, which is a labor cost people rarely account for in a DIY quote.
Edges do more visual work than the mulch itself. A re-cut bed line, a clean vertical spade edge, is what makes the front of a house read as maintained from the street. Fresh mulch inside a soft, migrating edge still looks unfinished.
On color: in full Houston sun everything fades. Black holds the longest, brown fades gracefully, and red is the first to go orange. Natural pine bark does not hold a dyed color at all but breaks down into something your soil actually wants. Pick based on how often you plan to refresh.