[Not sure if I should answer this, but I will try to answer something while trying hard to not go off-topic.]
Mercury surface is essentially a collection of small random craters with no discernible pattern at all, so you might not consider which side is presented. The only distinguished feature is a set of dark craters in its north pole.
Venus features few discernible aspects in visible light to the human eyes. There are only a few and faint distinguishable cloud bands, so you might also not consider which side is presented.
Earth is the most important, because it have continents and oceans with distinct designs. It also features a lot of clouds.
Mars has polar caps and a system of canyons. It's northern hemisphere is also much less cratered and has a lower altitude than its southern hemisphere, except that the greatest crater is in the southern hemisphere.
Jupiter has a banded structure of clouds covering the entire planet. It features a large red spot with some nearby fainter and smaller whiter spots.
Saturn also has a banded structure, which is faintier to Jupiter's structure but still clearly visible. It also features a curious hexagon on its north pole. But it is barely noticeable.
Uranus have very homogenous atmosphere (as seen in visible colors by human eyes), so it have almost no visible features to be drawn in your tatoo. Their presented side do not matters, because it is essentially a bland featureless ball.
Neptune has also few visible features. There are no more than a few cloud bands with low variation on color or hue. However there is a dark spot.
Saturn has an extensive system of rings, which also contains some defined gaps.
Jupiter, Uranus and Neptune also feature faint sets of rings (1, 2, 3). Uranus has a weird orientation, so its rings are not aligned with the orbital plane, but roughly perpendicular to it.
All the planets rotates at different velocities, so any side of them would do. No planet is showing always the same face to any other planet or to the Sun.
All of the planets, except Uranus, are rotating roughly in the same plane. So, their north is all pointing to a side and their south to another side (lets call those north/south axis Y). Their north-south axis is perpedicular to their planet-Sun axis (which we will call X). Uranus is special because at their summer/winter, its north/south axis points roughly to the Sun (i.e., in the X axis) and in its autumn/spring it is in a direction that is perpendicular to both X and Y (so it's the Z).
Also, don't forget the Sun. It may also feature flares and sunspots sometimes. The Sun rotates in the same way as most of the planets, with its north/south axis along the Y direction.
You might also be tempted to include the planets moons. Those are:
Earth's Moon, which always presents the same face to Earth.
Mars moons Phobos and Deimos.
Jupiter moons Io, Europa, Ganymede, Callisto, Amalthea and lots of smaller moons.
Saturn moons Titan, Rhea, Iapetus, Dione, Tethys, Enceladus, Mimas, Hyperion, Phoebe and lots of smaller moons.
Uranus moons Ariel, Umbriel, Titania, Oberon, Miranda and several smaller moons.
Neptune moons Triton, Proteus, Nereid and several smaller moons.
You can get more data (and also some images) about them here and also here.
Also, you might want to include the dwarf planets. The confirmed dwarf planets are Ceres, Pluto, Charon, Eris and Makemake. Ceres is located in the main asteroid belt. Although technically being a dwarf planet, for practical purposes Charon is Pluto's main satellite and they always shows the same face one to the other. Makemake and Eris are beyond Pluto.
To complete the Solar Sytem, you could also add other transneptunian objects (likely to also be dwarf planets) like Quaoar, Sedna, Haumea, Orcus, Salacia, 2002 MS4, 2007 OR10, 2012 VP113, 2010 GB174, 2004 XR190, 2000 CR105 and 2004 VN112. Those 12 transneptunian suspected dwarf planets, along with Eris and Makemake, are no more than singular dots of light on the telescopes, their appearance is unknown and even their size is known only crudely, with very large error margins in their size estimatives (see more about that below).
If you want also specific asteroids, you might see this page.
- The Sun's diameter is roughly 10 times Jupiter's diameter.
- Jupiter's diameter is almost 11 times Earth's diameter.
- Saturn has almost the size of Jupiter, having 9.5 Earth's diameters. Also, it is visibly oblate (oval).
- Uranus and Neptune are about the same size, with 4 times the Earth's diameter.
- Venus is almost the same size of Earth's (95% of Earth's diameter).
- Mars is a bit larger than a half of Earth's diameter (53%).
- Mercury's diameter is 38% of Earth's diameter.
- Moon has 27% of Earth's diameter.
- Pluto and Eris were determined to be essentially of the same size, which is 18.6% of Earth's diameter.
- Ceres has 14.8% of Earth's diameter.
- Charon has 9.5% Earth's diameter.
- All the others known transneptunian objects, although surely smaller than Pluto, have uncertain sizes.
- All the dwarf planets and asteroids are significantly smaller than the Moon. Check the links for more details.
- Some satellites of Jupiter, Saturn, Uranus and Neptune are pretty large. Titan and Ganymede are even larger than Mercury.
For more details about sizes, check this page.
About the transeptunian objects, only Pluto and Charon have a known appearance (due to being photographed by New Horizons). This way, all that you would need to draw in your tatoo beyond Pluto and Charon is a group of little spheres smaller than Pluto (I named 14 of them above), with only the one representing Eris with the same size as Pluto.
You will find images and further detailed information in the previous links, all of them points to wikipedia. I hope that you can get a perfect tatoo with that information!