Every fence material looks fine on installation day. The question worth asking is what it looks like in year eight, because that is where the real cost of a fence lives.
Wood is the Houston default, and for good reason: it is the cheapest way to get eight feet of privacy, and cedar or treated pine handles our climate reasonably well if it is built correctly. Correctly means pickets held off the ground, coated or galvanized fasteners, and posts set in concrete. Plan on staining or sealing it every few years. Skip that and our humidity will gray it out and start feeding the rot at the bottom of every board.
Vinyl costs more up front and asks for almost nothing afterward. It does not rot, termites have no interest in it, and a hose takes care of the annual cleaning. The failure mode with vinyl is not the panels, it is the posts: thin-wall posts and unreinforced gate posts are how a cheap vinyl fence ends up leaning after a storm season. Heavy-wall posts set deep, with steel reinforcement at every gate, is what makes the material live up to its reputation.
Ornamental iron and aluminum are what you install when you want the perimeter secured and the view kept. They handle wind better than any solid fence because the wind goes through instead of pushing. The thing to watch here is the coating, especially east of town toward the ship channel, where salt air will find any bare cut edge. Powder coat over properly prepped steel, or aluminum if you want to stop thinking about it entirely.
Chain link is the cheapest way to enclose a large area, and it is genuinely the right answer for back lots, side yards, dog runs, and job sites. Black or green vinyl-coated fabric disappears against a treeline far better than raw galvanized does. Whether it stays taut is entirely down to the install: terminal posts sized to the run, braced corners, and fabric that is actually stretched rather than hung.
One last thing that applies to all four: check your deed restrictions and HOA rules before you order material. Height limits, allowed materials, and which direction the finished side has to face are spelled out in a lot of Houston-area neighborhoods, and a fence that violates them is a fence you get to take back down.