Had a tiny map with rare everything, 1 AI player (random) and random intelligence with events on, and minor races on, and tech trade disabled. I played Terran and got Yor, no minor civs and only 12 habitable worlds.
If you're just learning, then more opponents is better. You can learn how to use diplomacy with/against a variety of races. Some are fodder as allies, some as purely tech-trade cash-cows, and one or two as targets of opportunity.
Bought a basic factory on earth 1st turn and landed my colony ship with 500M on Earth which had a pop of 1B.
Wow, what version of DL or DA are you playing? I don't remember 1 billion as the starting pop, and I've been playing since at least DL 1.3.
Bought a cargo hull and upgraded to a colony ship.
Why not just buy a colony ship? I'd think your approach would be more expensive. I've never done it though, so I could be wrong.
and 7 mines.
It will be very important for us to know whether you mean astroid mines or resource mines. And are you playing DL or DA? And what version?
After the rush phase I built a spare colony ship and began moving pop off Earth to Mars. At 12B (max pop) I moved 190M per turn without affecting Earth's pop.
Might as well fill that ship up. Were you building econ buildings on these planets? Earth will refill itself quickly and you'll get Mars going much faster with 500M instead of 198. Of course, if Earth is actually at 1 billion, then your approach is better at this point.
In around 30 turns I was a cash cow and began garrisoning my planets with cargohulls filled with weapons.
If you only have one opponent, then your military rating isn't going to be so important. Therefore, you might as well be building true warships, like small-hulled ships, instead of cargo-hull ships. Only use cargo ships as false military ratings boosters when you're worried that an opponent might attack with a much stronger force very soon. In fact, I've never used cargo hulls for such a purpose. I just build what I'll use in the future.
Now I think the game is basically over so I'll try another with 2 AI.
I wouldn't work my way up so slowly! It's actually better to have more AI much of the time. And you'll learn much more quickly if you learn to use the Foreign Relations aspects of the game. They are really a make-or-break aspect when you're playing on higher difficulties.
Go ahead and try a larger map (medium or large) with a lot of opponents. If you get annihilated, at least you'll learn much faster than this slow kind of approach.
Good luck to you, and keep us informed as to how you're doing.