Were Gram-positive rods the first bacteria?

At some point in the evolution of life, the domain Bacteria arose from prokaryotic progenitors. The cell that gave rise to the first bacterium has been given the name (among several other names) "last universal ancestor (LUA)". This cell had an extensive, well-developed suite of biochemical strategies that increased its ability to grow. The first bacterium is thought to have acquired a covering, called a sacculus or exoskeleton, that made it stress-resistant. This protected it from rupturing as a result of turgor pressure stress arising from the success of its metabolic abilities. So what were the properties of this cell's wall? Was it Gram-positive or Gram-negative? And was it a coccus or a rod?