For starters, I'd recommend turning off the DLC (ESPECIALLY megaevents, but I'd also suggest no precursor worlds) until you've won a few games and are looking for something extra to spice the game up. Precursor worlds are extremely powerful, but until you're confident that you can grab your fair share of them that just means you're making the AI a couple of difficulties higher.
First thing to do once you're actually in-game is go to the ship designer, and re-design the basic colony ship. The basic variant is loaded down with dozens of life support units which are, honestly, bloody useless. Strip the colonizer down to 1 life support and a colony module. Add a couple of sensors (these are our scouts as well as our colony ships), and then add as many engines as you like. With all engines added, it will move twice as fast as the default ship, and see an extra space in each direction, but will cost 20% more. It's usually worth the trade off.
Set your global wheel to 100% research, and then rush-buy factories until you run low on money. Leave space for a couple of farms (build these last) and a couple of entertainment buildings (near last; this planet will be depleting it's population fairly soon). Rush-buy a couple of colony ships in orbit at the same time. Feel free to spend yourself down to about 500 gold.
Ignore Mars with your first colony ship. Mars sucks, and can always be grabbed later - on or better yet culture-flipped from a careless enemy. Send the first colony ship out toward the nearest star. Send the second out to a different nearby star. Colonize 2 decent-sized (10+)planets. Cover one in research centers (+2 spots for farms, +2 spots for entertainment). Cover the other in markets (+2 farms, + 2 entertainment centres). Set them to manufacturing until they're built, then put them focused on the right resource and ignore them forever after.
Do not enter enemy influence. Your long-range sensors on the colony ships should allow you to meet other civs without entering their space til about turn 30 or so. This avoids penalties, which can spiral rapidly into game-long grudges.
Once the homeworld is covered in factories, stop rush-buying stuff. Reset the global wheel to 25% science, 75% industry. Set your homeworld's focus to manufacturing, and it should now be producing manufacturing at around 90% efficiency.
You are now going to fall behind in research until your research worlds can take up the slack. That's fine. No-one's getting invasion for a while anyway. The homeworld should begin pushing out a colony ship every 5-6 turns or so. You can colonize Mars now, if you like, to reduce the damage done to Earth's population levels by the Great Migration. And always send out the colony ships as empty as you can until around turn 100 or so. When a colony ship lands, set up the world as either manufacturing, research or econ, using roughly 1 econ world for every manufacturing world and 1 manufacturing world for every 2 research worlds. Every manufacturing world should build a shipyard last.
After 4-5 colony ships have gone out, you can throw in a constructor if you like, and build a starbase for your homeworld. You can toss in some scouts, too, but they're largely useless.
Unless you've encountered pirates, don't bother building military ships until your second shipyard is online. Do not panic if the AI starts to massively outgun you at this point. Other races will usually begin arming at around turn 20. The ships they make will be useless in combat and a horrible drain on their resources, but will not stand a chance against the ones we'll be building by the time they have planetary invasion. You can build your first warship when you have small hulls and some weapons tech; this will probably be around turn 50 or later. Set the second shipyard to just spam small warships. Garrison every planet with one, then a second, and repeat.
Your third shipyard will be dedicated to building constructors in peace time (and will be switched to making warships in war). Cover everything you can in starbases. Upgrade them as much as possible. This is tedious, but maximizes your advantage.
Once you have enough of a fleet to feel defended (ignore the military scores, your ships will be pound-for-pound far superior than the AI's), switch the global wheel over to 75% science and then just turtle until you've overtaken the AI's research in every relevant field. I'd advise going for the planet development techs first, once you have the basic ones from the other fields.
Then kill them, one at a time, starting with the weakest neighbouring civ. In wartime, or when preparing an invasion, your global wheel should be at 75% industry, 25% research to rapidly produce ships. In peacetime, it should be 75% research, 25% industry to rapidly develop tech. The only time when you should have any economy spending on the global wheel is when you have negative cash.