Yeah, drop pods (or landing shuttles).

That being said, the counter-argument would also be valid. Would it even make sense for a ground force without an established space superiority and logistics to be actually able to take over a world?

Valid concern. In my game yes. One race don't even have any fleet, they just take a big rock, drill tunnels, hop inside and then lanuch it to the neighbouring planet where it crashes and they leave and kill whatever they see. Other races can only try to shot down as many of these asteroids/rocks as they can, but even damaged one guarantees survival of a percentage of the "passengers". That race is non humanoid and highly resistant and don't require supply (other than the enemy which is considered very nutritious) :)

As for more traditional invaders, if they are able to take part of the planet they can get some local supplies I suppose?

Plus, no space superiority does not necessarily mean they can't drop supplies for them somehow (it does not need to work like in WWII). Anyway, they should at least get a penalty if there is enemy superior forced above them (especially for invaders).

Anyway, I wonder about exact mechanics of the troop transport and defender's anti-pod fire.

Something along these lines maybe...:

- when you invade a planet you bring combat ships and transport ships, the combat ones fight and the transport ones are safe (can't be fired upon by anyone, they just occupy the space and wait).

- if your combat fleet is destroyed (or too weak) enemy can fire on your transports

- your transports do nothing by default, but if certain conditions are meet (like enemy fleet destroyed and planeteryu anti pod defence is suppressed) they will auto start dropping troops, also you have an option to manually drop trops anytime (regardles of conditions).

- when the troops are dropped first enemy fleet (if present) will fire at these (as a priority), then planetary defence fires on these pods. Even under heavy defence there at least 10-25% of troops are guaranteed to land succesfully (not sure how to calculate this), so you neven have 100% defence agains drops, you need to have some defensive troops/bunkers to deal with unavoidable succesfull transits (if it makes sense for the invader to lose 90% of troops upon landing).

- then a normal ground battle starts (you can bring reinforcements anytime the same way).

You could have it play out like a chess board:

O = Armed ship

# = Cargo pod

X = Enemy defender

# X

#O X

#OO X

#O X

# X

In the above graph, the X on the outer edges would be able to strike at undefended pods on the sides, but the middle is fairly well defended so the player might just make a breach for their pods using forward ships.

The row with two "O"s would take out the X, and the pod would reach the end.

These extra "O"s could reinforce pods that are vulnerable as the row becomes empty of enemy X...

It would feel a bit like Plants vs Zombie actually :P

In parallel, or sequentially after determining how many pods got through, you could simulate ground invasion based on the amount of Os that got through.

I might actually use a similar system :S