As stated, water chemistry matters most for all grain beers, and to a lesser extent, partial mash recipes. The actual pH of your water matters less than the hardness and alkalinity, however, because they determine your mash pH (that is the most important parameter when brewing from grains).
Most municipal water supplies are pretty good, though, and you likely don't have to worry. If your water tastes good, it will probably brew good beer. Just be sure to filter it or treat it to remove any chlorine products.
Regarding dissolved oxygen, the optimal levels depend on the gravity of the brew. 8 ppm is usually sufficient, and that can be achieved by shaking your cooled wort in a carboy for 2 - 3 minutes. If you need to go higher than that (e.g., for a high gravity Belgian trippel), then you need to oxygenate with compressed O2 and a diffusion stone.