For most homes, AUTO is a sensible starting point: the indoor fan runs with a heating or cooling call. ON keeps air moving even when the compressor is not cooling. The better choice depends on comfort, the system and moisture behavior in your home.
On a humid Texas day, continuous fan operation can move moisture left on a cooling coil back into the air after a cooling cycle. That may leave a room feeling clammy even though the thermostat temperature looks fine. It does not happen to every system in exactly the same way, and a fan setting is only one possible part of a humidity problem.
AUTO usually means the fan stops between calls. It can reduce fan runtime and may help avoid re-evaporation from a wet coil. ON can make air movement feel more even and can be useful when a system is designed for continuous circulation or filtration. It also uses electricity for the extra fan hours. Follow your equipment and thermostat instructions, especially if you have a variable-speed system or special ventilation setup.
Try a simple comparison instead of changing several settings at once. Leave cooling set point the same, note indoor temperature and humidity, and compare comfort over similar weather conditions. Make sure the filter is installed correctly. If one room remains much hotter, the fan switch alone will not fix a duct, insulation or solar-gain issue.
Along the Gulf Coast, moisture is often a more visible part of the comfort question than it is in drier Far West Texas. That regional difference is a reason to observe your own home, not a rule that every Texas thermostat should use one setting year-round.
If humidity stays high, water appears near equipment, or the AC cycles rapidly, use those specific guides and ask a professional to assess the system. Never open electrical panels or alter wiring to test a fan mode.
A fan setting also cannot tell you whether the system is sized or configured appropriately. If you are comparing bills, record the setting and weather along with your energy use; a single bill combines many other changes. If your thermostat offers a circulation setting, consult its manual because that option may behave differently from a simple ON switch.