For some of my lenses, I need to stop down a bit for optimal sharpness. In general, that is a good idea if you can, but I don't feel a particular need to do this with the 18-105. Maybe if I had to guess, f8. I shoot it wide open often with no issues. Like Mike said, you may have other priorities like needing a greater or lesser depth of field.
Shutter speed is more up to you. Tripod, hand held, desire to show motion, desire to freeze motion, desire to use a certain aperture, etc; your needs will vary. If you are after sharpness, fast is better especially hand held. Handheld go with minimum of 1/focal length. Some will say 1/(1.5*focal length) to take into account crop factor. In the end it depends on technique too. For the absolute sharpest shot, I'd want a good bit higher speed than 1/FL. You want to overcome camera shake and you may need to freeze some subject motion due to wind or whatever. So no perfect shutter speed.
Just go out and shoot a bunch. Save your pictures even if you are unhappy with them until you have learned all you can from the shot.
You say you are new to SLR, are you fully comfortable with the principals of exposure? I'm talking the relationship of shutter, aperture and iso? If not, you must get familiar with those things. Also learn and understand your camera's focus modes.
