Mulch is the highest-return thing you can do to a Houston bed. It holds soil moisture through a month with no rain, keeps the root zone measurably cooler in August, blocks most weed seed from germinating, and makes an ordinary bed read as finished. It is also the job most often done wrong.
Depth is the first thing people get wrong. Three inches is the target for a hardwood mulch — under two and light reaches the soil and the weeds come through anyway; over four and water starts running off the top instead of soaking in, and the layer stays soggy underneath. To work out how much you need, take the bed's square footage, multiply by the depth in inches, and divide by 324. That gives you cubic yards.
The second mistake is more expensive: piling mulch up against trunks and stems. It holds moisture right where the bark needs to stay dry, and over a couple of seasons it rots the collar of the plant you were trying to protect. Pull it back a few inches from every trunk and stem. The bed still looks finished, and the shrub survives.
On timing, once a year is usually enough in Houston, done in early spring before the growth starts. Do not just dump new mulch on top of the old — the old layer compacts into a mat that sheds water. Break it up first, pull the weeds while the bed is open, re-cut the edge, then top up to depth.
Pine straw is worth mentioning because it suits parts of this area better than hardwood. It knits together instead of floating, which means it stays put on a slope and after heavy rain, and it looks right in the pine-heavy neighborhoods north of the city.