Since No Man's Sky doesn't allow for multiple Gas Giants within a system, I'll assume the following would be closest and skip the gas and ice giants, for uhh... travel time purposes! (And totally not because in NMS they don't spawn on G-type yellow stars).
That is;
• Single, Yellow G2V-type star
• Low/No Sentinels on any worlds
• 6 worlds, 1 Moon
- Mercury (Dead; grey)
- Venus (Scorched; yellow air with dark rocks, as few flora/fauna as possible. No water. Weather: Extreme)
- Earth (Lush, Paradise; blue sky and water, sandy-like beaches, green-brownish land with normal animals and plants. Weather: Clear)
- Moon (Dead moon, grey)
- Mars (Irradiated, as few flora/fauna as possible. No water. Weather: Normal)
Optional extra
If we still want to include some of the ice/gas giants, we could pretend the Sun to be an X-type 'purple' star, as their temperature isn't given. In that case:
- Jupiter (Waterworld. Weather: Extreme. Light brown with a ring).
- Saturn (Waterworld. Weather: Extreme. Yellowish with a ring).
- Titan (Moon; Toxic biome. Weather: Clear. Yellowish atmosphere, light brown ground, dark "water", ie. methane).
I picked Titan 'cus, it's fun and one of the more likely candidatea to eventually develop life, and it has lakes!
I'm not sure if this idea list could be improved or not, but might be a fun challenge for the community. It makes me think, maybe HelloGames should add in a possibility for 'small' Gas Giants, so that those can be generated in systems with more planets.
And I don't know if there are non-Dead planets without flora and fauna, but they totes should be a thing.
I don't know how long you have been playing nms, but every few years they have been releasing big updates that often change multiple planets.
To the degree of replacing features and fauna.
So that happens.
I don't know of a system like our solar system. But even if you find one, it probably will change at some point in the future and stop matching.