growing up we had either Blue Dawn or Green Palmolive at every sink in the house, it was way cheaper than the hand soap
I've inherited that and we've got Method dish soap for hands at all the sinks (we like the scents) and Blue Dawn Platinum for the dishes (mostly knives and the odd pot that I'd rather wash than wait for another dishwasher load.) For showers and tubs: Dawn, vinegar, and a touch of cornstarch equals almost no scrubbing! I've heard the Dawn Powerwash is also fantastic for showers and tubs.