Navy + Air Force
Nobody likes to attack a fortress, because that's where all the enemy's guns and armor are located. A navy lets a military bring their fortresses to the battle front. Water can carry much bigger guns and much heavier armor than land can. That's why tanks only carry one 105 mm gun, but ships can carry 9-12 guns at 460 mm or more. An air force, on the other hand, allows a military to deliver fires quickly and deep within enemy territory. Ballistic guns generally max out at less than 50 km.
Land forces encountering an enemy fight a mostly 1-dimensional conflict along the front, with elevation providing a minor 2nd dimension, unless one combatant is able to out-maneuver the other by flanking/pincer/surrounding, in which case the battle is clearly 2-dimensional. Air forces guarantee that the conflict is always 2-dimensional, and that assets are vulnerable anywhere on the battlefield.
A space navy, on the other hand, combines both these aspects of a planetary navy and air force: they enable the military to "bring their fortresses to the front" as well as "project power over the entire surface". But a space navy only needs guns to deal with other space navies. As far as folks on the ground are concerned, the altitude alone is the threat. And this is why you can't use Terran history to extrapolate the effectiveness of space forces.
If genocide is your goal, because your society has decided that it can never co-exist peacefully with the enemy, then it is sufficient to bombard the enemy into oblivion. If you can tug big rocks around space, then "bombardment" is as simple as choosing a suitably large rock and dropping it on the planet. This is boring.
Most armies do not have genocide as their goal, because enemy civilians are potentially useful assets, along with the resources they hoard/harvest/mine. Getting those civilians to do what you want is pretty difficult with a navy or an air force, because the scale of firepower is inappropriate. If a farmer isn't growing crops for you, dropping a 2000 lb. JDAM on his head isn't going to achieve your goal. Holding some valued members of his family hostage, on the other hand, can be a pretty powerful motivator. For that, you need boots on the ground.
In fact, history is full of successfully invading armies taking over territory. From Alexander the Great and Genghis Khan to the founding of America to Iraq. Boots and guns have been very effective at projecting force onto a civilian population and subjugating other peoples. Sure, there will be resistance of varying levels depending the technology and resources available to both sides. But invaders which want to maximize assimilation rates will deploy propaganda and soft power to subvert and co-opt the resistance, in addition to the boots and guns which remind folks who holds all the cards.
If you have two evenly matched forces, then we expect any conflict to start in space, because each navy will try to interdict the other as it targets valuable assets. If the navies are competently commanded, then they may reach a stalemate and a detente. If one is overpowering, or simply executes better strategy, then eventually the other navy will succumb and eventually become ineffective.
At that point, what is stopping the dominant navy from flying straight to the capital planet or other major city worlds, and threatening the populations there with catastrophic bombardment? The aggressor simply needs to threaten to exterminate all life on the planet in order for the defender to unconditionally surrender and sue for peace. If there is any doubt about the ability or willingness of the aggressor to destroy targets on the valuable capital planet, they just need to pick an expendable target highly valued by the defender but otherwise useless to the aggressor, and obliterate it from orbit. Even if the planet has its own counter-orbital batteries, they cannot realistically defend against an entire navy which is free to choose its orbits and drop rocks wherever they like. And such batteries would obviously be the first targets for the invading navy. Even if the batteries could vaporize a meteor or two, it is always possible to pick a rock big enough that it cannot vaporize it before it impacts. Or, to drop more rocks simultaneously, from different approach vectors, than the defenses could possibly intercept. Note that the blockading navy can drop literal rocks. No need for fancy missiles or bombs or expending energy on beam weapons to target stuff on the ground.
Once the capital sues for peace, the aggressors just land their army "to enforce the terms of the treaty" and secure valuable shipments that are headed off-world, as well as keep a close eye on leaders who might have designs on running a resistance campaign. It should be expected that independent groups will run resistance efforts anyway, and thus, the army would be expected to secure the most valuable facilities and defend them against guerrilla attacks. Some resistance groups may be able to muster competent battalions of fighters and give the army something interesting to do, but the invading army would also be expected to have full air superiority at its disposal, not to mention orbital support for particularly intransigent defenders. Remember Vichy France.
Of course, a space-faring military would not even bother to think of separating Army and Air Force. Rather, it would think in terms of "interplanetary" and "planetside" forces. And that's why you would end up with just a Navy and an Army. And why the Army should be able to subdue any planet with an uncontested orbiting Navy.
Unlike some other answers, the Army would not just be responsible for "mop-up" operations. While it isn't going to project the majority of force (that comes from sitting at the top of the gravity well), it will project force most precisely and most intimately with the subjugated population. It is the force which will determine which citizens will become enemies or allies of the aggressor civilization. Sometimes, this may involve full-scale planetside battles, if the Capital planet breaks up into competing factions, and the nominal leading faction sues for peace, but the other factions decide to fight while holding on to valuable assets. Orbital bombardment is always a last resort, but in some cases, it may be necessary to fight full scale planetside battles to convince the resistance that their efforts are futile, and the aggressor has overwhelming force at all scales.