DOF is related to the aperature, so as suggested use a higher aperature (f11 or higher). A faster shutter speed and lower apeture should only be used for motion or low light, or when you want a shallow DOF.

Removing noise in Photoshop is quite tricky. Instead, use Neat Image or similar software, but be careful not to overuse it. The images can turn out muddy or have a plastic appearance. If there is only a little bit of noise. all you have to do is use the blur tool to smooth it out instead of applying noise reduction to the entire image.

And never use auto settings! Always go with manual, because you have greater control of the camera. Some of my noisiest images were shot in auto mode.