The moon will appear most spectacular right around moonrise, though this is largely due to an optical illusion rather than to its closer proximity. The exact cause of this illusion is debated. One theory is that the presence of objects, such as trees or buildings in the foreground, make the eye focus differently, and another holds that the brain interprets distant objects as wider.
Since the earth tides (both in the solid earth and in its oceans) are caused by the gravitational attraction of the moon and sun (mostly the moon), tides are expected to be higher than normal, but not by enough to get all excited about. NASA estimates about 1" higher than usual, possibly somewhat higher depending on local geography, and also amplified if there are storms in the area.
Example of amplified tides due to supermoon. This record,
extracted from a NASA video of a longer time-record.
One is on Io, a satellite of Jupiter. The gravity of Jupiter and its largest moon Ganymede, with help from two other moons Europa and Ganymede, cause tides over 300 feet, as high as a 30 story building. This deformation causes such heating in the interior of Io that it spouts fiery volcanoes of sulfur and sulfur dioxide. The other is on Enceladus, a frigid satellite of Saturn. Enceladus is only 80 K, 80 degrees above absolute zero, at its equator, but at its south pole, temperatures as high as 180 K have been measured. In that region, icy plumes of water ice spurt out into the vacuum of space. The tides on Io and their effect in producing volcanism were figured out by three scientists*** even before the Voyager spacecraft arrived there and observed the volcanism. The tides on Enceladus and their relation to the plumes are still not fully understood. Two different satellites, two different manifestations of tidal energy.
**Here is an excellent article about the event from EarthSky.org.
***Peale, Cassen, Reynolds, Science, 203, 4383, pp. 892-894, 1979