I don't have a specific start I always do, but I can win on King, level 6 right? When I'm trying out new Civs or tactics I prefer a lower level.
I tried the national college start, but I prefer to be more flexible and adaptable. I play on random maps and take whatever start I get. Generally I look at what luxury is nearby and research that tech first or quickly. I also like to build a monument first but I will sometimes build a warrior or scout depending on my estimate of the size of the continent/island I'm on.
If you're Babylon you want to research archery promptly. Same if you are the Inca. With you're better bowman you can hold off barbs and warrior rushes. I generally prefer Liberty, pretty much all of Liberty then if you're happiness is OK, Patronage. If you need happiness or you're trying for the cultural victory take Piety. Lately if disciplined you can choose Freedom or if you prefer Rationalism. The free settler and/or worker is huge as is making them cheaper. I tend to go worker first, but if you find a great city site and your happiness is 5ish you can settle a second city quickly, just make sure you can defend two cities.
I'm not much of a warmonger, but if you are on a smallish island with one other Civ you have to prepare for war. I try to put my second city in a strong defensive position. I am a big trader and leverage city states. They can help a bit in a war but are better for food and culture in peace time.
Generally you can't expand too much beyond 3 or 4 cities until you're ready to fight a war. Besides archery, mining, writing, and philosophy are key early techs. If you get a tiny island start you need to bee-line for Optics ASAP. Rarely do I have enough Iron to build lots of swordsman and I prefer to use my limited iron on trebuchets. I don't like trying to conquer cities without them, but it of course can be done. Crossbows + Trebuchets + one or two assault unit is how I take cities. Great Generals are also key, doubly so or is it +25% so if you're China. Prior to having those techs I fight defensively and rely on walls and favorable terrain.
Babylon is a good civ for my style, but so is Arabia, and China. I also like Polynesia, Rome, Greece, and Siam.
Basically you can prioritize techs, but don't assume you'll get to build any particular wonder, you often have to settle for a wonder, and use great engineers to snap build them. Liberty and other means of getting free great people or a social policy are very valuable. You can get a free great general from Honor which is something I use in a pinch. Lately I haven't been using Tradition much at all, but folks on this board advocate holding off and use the policy that gets you free cultural buildings late in the game to get free museums. Tactics like that are all well and find on discussion boards, but getting to the medieval ages or Renaissance with a chance to win is more of a priority. For that you need a measured expansion policy, defensible positions, and likely a few key military tech.
Depending on who your neighbors are it is possible to be a good neighbor and go most of the game if not the entire game on Level 6 with no wars.