Here's a suggestion: do the Kerbal Space Program system. It's just seventeen objects.

Kerbol - the Sun
Moho - Mercury
Eve - Venus
Gilly - moon of Eve (no real-life equivalent)
Kerbin - Earth
Mun - the Moon
Minmus - captured comet, moon of Kerbin (no real-life equivalent)
Duna - Mars
Ike - Binary partner of Duna (no real-life equivalent)
Dres - asteroid/dwarf planet 1 Ceres
Jool - Jupiter
Laythe - Oceanic moon of Jool (no real-life equivalent)
Vall - Europa, moon of Jupiter
Tylo - Ganymede, moon of Jupiter
Bop - Captured asteroid, possibly Himalia?
Pol - Captured asteroid, possibly Valetudo?
Eeloo - asteroid/dwarf planet 134340 Pluto

If possible, add in the Outer Planets Mod for KSP. It's an additional fifteen objects.

Sarnus - Saturn
Hale - Pan, moon of Saturn
Ovok - Methone, moon of Saturn
Slate - Desert moon of Sarnus (no real-life equivalent)
Tekto - Titan, moon of Saturn
Urlum - Uranus
Polta - Miranda, moon of Uranus?
Priax - Lagrangian companion of Polta, lags 60° behind (no real-life equivalent)
Wal - Titania/Oberon, moon of Uranus?
Tal - Sub-moon of Wal (no real-life equivalent)
Neidon - Neptune
Thatmo - Triton, moon of Neptune
Nissee - Nereid, moon of Neptune
Plock - asteroid/dwarf planet 134340 Pluto
Karen - Charon, moon of asteroid/dwarf planet 134340 Pluto