What kind of texture? Most "textured" walls can be painted with a roller. The knapp you choose will depend upon the depth of the texture. Your sponging idea could work, if you are looking for that effect. The very best advice you could get on this topic is to go to your local Sherwin Williams or other actual PAINT store, (NOT a big box warehouse store) and talk to them about your project. They are in the business of teaching you how to do these things so they can sell you the things you need to do it with. Do not "save money" on paint. Buy the very best they have, because you only want to do this ONCE. I recommend avoiding flat paint because it is much harder to wash, but I also avoid gloss finishes because they show EVERY imperfection in the wall. Choose something inbetween.