How big is the house? How many rooms? Pictures? A window A/C unit in a back bedroom will cool the bedroom it is in but it is unlikely to cool the rest of the house adequately. Is there an attic available for air handling equipment? Do you have a closet to put an indoor air handler in? From either, then run high velocity ducting up and over to each room? Refrigerant lines can be brought out through the eaves, they don't have to pass through walls. There are several ways to approach your A/C need, you really need a trained pro to come in and evaluate the situation.

The best way in Texas is forced air with ducts. If due to the construction / age of the home makes this unfeasible you are looking at serious costs to retro fit.

Mini splits can be the same situation with maybe a marginal degree better... because you will have cooling heads in every room of the house... so instead of running ducts they run refrigerant lines to every head.

If you don't have room to install a cassette in the ceiling then you have an ugly looking box on the wall in every room you want cooled. (If you have the room to install the cassette, you have the room to run ducts most likely.)

Due to run times of HVAC equipment in Texas the more equipment you have, the more it will cost to maintain it, repair it and eventually replace it.

So you will get varying opinions each with their own list of pros and cons.

I service the Katy, Texas area.

What type of ceiling and attic do you have?

Mini-split cassettes can be mounted in the ceiling (they look like a fairly large square vent), or its very common in TX to install an A/C system in the attic with ducts in the ceiling. I've also seen high velocity ducted system in historic buildings, since the diameter of the duct is much smaller and it is easier to hide/blend in.

All of them need a compressor outside, and you need about a 5" hole in the wall for the two copper A/C lines. However, many times you can hide the hole and the lines by running them along trim boards or up againsts downspouts.

In your climate you could also use a heat pump so that you get both heat and A/C. Heat may not work as well when you use ceiling ducts, but its done very frequently in warmer climates.

Bruce