You'll want to consider the timing of which night to shoot the moon. The moon is past the first quarter and approaching full. When it's "full" you don't get the shadows and that means the moon looks rather plain, flat, 2-dimensional. When it's nearer to first or last quarter the sunlight is illuminating from the side and that means you get lots of shadow detail near the terminator that separates the light and dark sides -- you'll see more texture and will appear more 3-dimensional.
The full moon is this Sunday, July 9. If you wanted to shoot moonrise you can get a dramatic shot around 30 minutes or so after sunset during the "blue hour". The "golden hour" is the hour prior to sunset when the sun is low and the lighting is golden. After sunset, we get the "blue hour" when the sky is a dusky blue color and still enough light to illuminate the foreground. This gives you foreground interest (it's not just a moon in an otherwise black frame) but the sky has had time to darken to a dusky blue instead of the pale blue of full sun.
Shooting a full-moon moonrise usually actually looks best the 1 day PRIOR to the true full-moon. So that would be Saturday, July 8 because the moon will be rising enough to be in the sky when the sky is still dusky blue. A day later and the sky will be nearly black by the time the moon is high enough. The moon still looks "full" even a day before or after the true day of the full moon. But it will also look "flat" and 2-dimensional.
If you wait say... 5 days or so after the full moon (waning gibbous phase) or even a full week (last quarter phase) then you'll get more detail, but remember that the moon rises nearly 1 hour later each day. This means the moon won't be up in the evening... instead it will be rising several hours before dawn. You might be waking up at 2 or 3 am to get the moon shot (which is why you see FAR more moon shots of the first quarter as compared to the last quarter phase).
For the moon... the exposure guideline is the "Looney 11" rule which suggests that you'll get an accurate exposure if you use f/11 with the shutter speed set to the inverse of the ISO setting. E.g. at ISO 100 use 1/100th... at ISO 200 use 1/200th, etc.
The moon's true reflectivity is roughly the gray of a worn asphalt road or the gray of an old tire. It shouldn't be particularly bright.
The camera's phase-detect auto-focus won't work at f/11 (it won't work at any f-stop above f/5.6) so you'll need to use manual focus. You can refine focus by going into live-view and then zoom in to the 10x level and very gently tweak focus until the moon is tack sharp (don't just rely on using the "infinity" mark on your lens focus ring. That would get you close, but it won't be bang-on accurate.)
You'll also probably get better results if you can steady the camera (a tripod if you have one... if not find something like a fence or wall that you can use to prop up the lens.)
This was shot following the "looney 11" rule (ISO 100, 1/100th sec at f/11) exposure... but then adjusted in post processing to increase contrast (the "straight out of the camera shot" doesn't pop as much.)

Waxing Crescent Moon by
Tim Campbell, on Flickr