These good old fashioned sponges are still the best. They last a long time, and can clean most anything. If you need anything heavier, get SOS or Brillo pads. The scouring side is tough and abrasive, and the soft side finishes the job. Other "newer" style sponges don't have near the scouring power these do. And "dobies" are pretty much only good for scouring, 'cuz they don't have a soft side. They also don't last as long.
Sponges do gather bacteria like anything else you keep in your sink. If they start to smell, all you have to do is put them on a plate, scouring side down, fill them with water until they're "full" to the point where water runs onto the plate, and nuke them in the microwave for 1-2 minutes. Wait five minutes, take them out, and you have a brand new sponge! You can do that every week, and they'll last you a while.