You can also set a lower number of planets, right now I play on gigantic and my civ only has a dozen planets or so, being the largest already. Depends on how you like it.
Look at the bonuses of your race. They should define your tactics. I generally choose a rather even mix of economic and domestic stuff, industrial and economic (+20%), morale (+10%), pop growth (+5-10%) research (+10%), luck (+25%) etc. Including party effects of course. A good economy is fundamental, and I didn't choose combat bonuses (except luck) so far. If you get your economy running, you have won the game.
The goal is: Spam colony ships. Design them to be at least speed 3. Have your expenses at 100%. The idea is to get out as many colony ships as possible while just skirting bankruptcy. To that end, don't fill your colony ships up to the max, but only put 100-250 mil into thém, not 500. Tax the populace to the hilt (40-50 approval), you don't need happiness you need planets. Planets Planets Planets.
Put a mix of buidlings on the home planet, factories should be first, the rest economy and research.
If you choose different bonuses you need different tactics. If you have a huge pop growth bonus you need to have your approval high to really benefit, at 100% your planets grow twice as fast. That means you can put more people on the colonies, and your tax income will soar after a short while. Don't forget approval bonuses too.
Think about where you send your colony ships. Chose their courses in a way to uncover as many solar systems as possible in the least time. Remember you only need to uncover the sun, not all planets, click on it and see how many habitables are present, if none, move on to the next system.
After you have your first 2 or 3 colony ships on the run (ion drive), ramp up your research spending. Research cartography, trade, xeno-economics up to where you get the better economy building, and space militarization and some weapon tech. Get all of this as quickly as possible, then lower your research spending again and go for social and military production again. Build your labs and econ buildings on the colonies and the home world quickly. After you get trade, gift it to the other civs for free, and if they already have it, a low amount of money. Show them you like them, and they will want to be your friend. Some are bad people though, and you need to deter them.
After you have no more planets to colonize immediately, build some small defenders, ships with no drive and a single small weapon. Build one for each colony, and park it in orbit. The other civs are disencouraged to attack when they see you have armed ships and are not a total pushover. I made the mistake in the beginning to, thought I don't need a navy, but then some evil minor race attacked me and I couldn't stand up to them!
Then build some freighters and send them to your neighbors. They like that.
If you are really friendly to other races, it might even happen that there's no war at all. In my current game the only evil dudes are the Drengin, and they lucked out in the colony race, so they don't really dare to attack their neighbors.