I am new to the game, but I had to wonder about the complete lack of moons.
My suggestion is this:
1. Each planet of size small or larger possesses the potential to have a moon. Each moon must be at least 1 size smaller than the parent planet. Small planets may have no more than 1 moon, normal planets 2, large 4, huge 8, and gas giants 16 (I know that gas giants can have more, but most of these moons have no appreciable size). In addition, gas giants may have a planetary ring (an asteroid belt around the planet). The chance for a moon should be extremely low for smaller planets, with most of the moons concentrated around gas giants. Asteroid belts cannot have moons, obviously, and tiny planets do not have the mass to hold an appreciable moon. I recommend a 1% chance for small worlds, a 5% chance for normal worlds, a 20% chance for large, a 60% chance for huge, and a 99% chance for gas giants.
2. Each moon should have a 90% chance of being barren, toxic, inferno, or radiated. They should have a 9% chance of tundra or swamp, a .9% chance of desert or ocean, a .09% chance of being terran, and a .01% chance of being Gaian. Additionally, each gas giant moon should have a (total number of moons/16) chance of being a planetary ring instead.
3. Every moon should possess at least 1 trait per size catagory difference between the moon and the planet. These traits should be weighted towards undesirable traits, such as tidal lock, high axial tilt etc.
4. Moons can be indicated by a line underneath the production indicators. A click reveals the moon icons the same way that a click reveals the production bars. This would prevent a planet-dense system with high lunar body density from taking an hour to scroll across. The number and type of moon could be displayed on the reduced bar. Icons for lunar traits would only show on the expanded bar.
5. Each moon should be treated as 1 catagory less on the suitable for colonization scale, due to the large planetary body that they orbit. The exception, of course, is gaian.
6. Moons cannot build orbitals due to the interference of the planetary gravity well. Each moon takes the place of 1 potential orbital station.
7. Moons can mount any planetary defense systems that planets can, such as planetary shields and ground-to-orbit weapons systems.
8. Moons have a stabilizing effect on their mother planet. This would be shown as a trait icon under the planet, with a small but appreciable bonus to the productivity of the planet. Alternately, the existance of one or more moons around a planet could remove 1 undesirable trait from that planet, determined randomly.
Also, I would like to suggest adding meteor showers and comets. Meteor showers could be a randomly assigned trait for some planets that adds mineral resources and research while detracting from agriculture and industry. The adjustments for these would be small. As for comets, their presence would result in a slight chance of deep impact (as a disaster). Deep impacts would destroy a random percentage of all improvements, kill a random percentage of the population, and destroy a random percentage of surviving production. The damage could be rebuilt in time, if some of the population survives.
I know that these items might have been beaten to death already in discussion, but I feel that their presence would provide the potential for an otherwise marginal system to become worthwhile. In addition, the increased resources of that system would make it strategically valuable compared to a system without heavy lunar concentrations.
One final question. Will you be looking at binary and trinary stars? If the star type has an effect on the planet count, then a binary or trinary star would stand a chance of more planets, while the effect of the stellar temperature could change the types of planets found in the system.