Game difficulty for Colony missions are increased the moment you research weapons. Starship missions, it is consistently hard; if you refuse to research weapons, then when the enemy sends his first wave of 3 microwave lynxes, they'll go straight for your command center and kill you. But, if you delay researching weapons in Colony missions, then Plymouth doesn't come. However, I believe that there are a lot of technologies that are locked off until you research weapons (as they require researching Mobile Weapons Platform), so you can't exactly avoid Plymouth forever.
As for the Starship mission, I tend to rush making about 9 Laser Lynxes, and destroy the enemy's main base before they can even build the majority of their walls or turrets. Once the main base is gone, the player has a lot more breathing room, as the expansion bases will take some time to develop their armies, allowing the player to focus on colony matters and better weapons. Whereas the main base, always sends the bulk of the attacking forces, so getting rid of it first significantly reduces the missions difficulty; also as the volcanic eruption makes it very easy for the main base to funnel your forces down a narrow walled trench with turrets blasting at you, you really will want to kill the base before that happens, otherwise you will suffer insane attrition losses trying to break through it. Hence why I destroy the base before it has a chance to succeed. Simplest way I found was to blow up the common smelter or both it's tokamaks in the early game.