I've had a fair amount of experience with conquering planets, including one defended by an army roughly 2 million in size on a forested rift valley world too cold for my species to live on, so I'll chime in with a few thoughts.
The size of the army you need depends most crucially on relative technology level. From fighting enemy ships, and possibly from a raid or two on an outpost or minor world, you should be able to make a decent guess about how this stacks up against your own. I'll throw out some estimates based on the assumption of equal tech, but having better armour than the enemy has guns will improve the situation drastically.
The second most important factor is planetary environment. You must always plan around this, because the size and composition of the hammer you need to wield will depend importantly on, for example, whether the temperature is too hot or cold for your species, or the presence of jungles or mountains.
Now, let's get to some estimates.
You see 10k enemy ground force signal on a flat, unforested world with a temperate climate. First, multiply this value by your best guess about fortification level. This will range from x2-3 for mechanized units to x6 for infantry or static with construction equipment. I usually use a multiplier of 4. So, guess 40k-worth of opposition.
Now, multiply again by the greater difficulty of hitting fortified troops. We won't get into math better explained in a guide, so let's just multiply by 2 (same firepower, roughly 4x as hard to hit). So, a 10k signal means the equivalent of very roughly 80k in an even fight.
If you drop an equal-tech army at least 2x that, then provided you have an effective unit mix and you include enough supplies, you can ordinarily expect to win comfortably. So, that's a call for 160k troops to defeat a 10k enemy ground troop signal.
Now, consider a planet with unfavorable environmental conditions. It might be too cold or hot. It might have rift valleys or mountains. It might be covered in jungles or deserts, have low gravity, or even have a Venusian atmosphere. I use the following multipliers; other players will use somewhat different ones.
Too cold or hot: 1.5x, unless your units have the Extreme Climate capability. This condition is quite common - watch out for it.
Forested: 1.25x, and bring 1.5x-2x supplies.
Jungle: 1.33x, and bring 2-3x more supplies. If your army has jungle training, then the modifier drops to not much more than 1x, because enemy non-infantry units are much less effective here.
Mountain: 1.5x, and bring 1.5-2x more supplies. If your army has mountain training, then the modifier drops to 1x or a bit more.
Rift Valley: 1.25x, and bring 1.5x supplies. Same comments as with jungles and mountains on the great advantage of well-trained infantry.
Dense atmosphere: 1.5x, unless your units have the Extreme Pressure capability.
Finally, let's talk about tech. By the time I get around to invading other races, my tech tends to be quite a bit higher than theirs. For every tech level you have over the enemy, multiply the size of the army you need by (very roughly) two-thirds. This varies depending on how carefully you maximize your advantages in penetration, damage, armor, and hitpoints over the enemy.
That two million-size army I mentioned earlier? Using an only partially optimized force, I took it down pretty comfortably with a total drop of about the same size (including all supplies), because I had at least a three tech level advantage over the defenders.