I'm not exactly great at this game, but there are a couple things I've found out since playing
-Worker first is almost always your best first build in the cap. An exception would be with a nice Seafood start (like, dual Fish or Fish + Clam/Crab), especially if you are a civ that starts with Fishing tech. If not, you can put hammers in a worker still while you tech Fishing (you'll alway need workers) and then start on your workboat(s).
-VERY important techs to grab early are The Wheel, Mining, Bronze Working and Writing, and should be prioritized after making sure you have your early food techs (Fishing, Agriculture, Animal Husbandry) that apply to your start. Wheel is the start to Pottery (for cottages and granaries) and lets you build roads, which is something you're going to NEED to have at some point for trade routes, hooking resources etc, often sooner than later. In fact, if I can't determine exactly what I need to do most at the moment and still don't have it, I snag it it next without thinking, it's that important. Mining lets you mine hills (and use certain resources), your all important sources of very early production and you need it for bronze working, which leads into the next point. Bronze Working is first and foremost the tech for Slavery, one of the most powerful and certainly the most impactful civics to any game. It also lets you crucially chop forests, which varies in importance based on how many there are and what you want to improve, but suffice to say it's a free production boost at your discretion and you can't improve tiles under them until they are chopped away. Writing is the tech that marks your transition out of the open stages and provides Libraries for running your first specialists (scientists), gets your foot in the door on diplomacy through open borders/resource trades, and is a prereq for a handful of next tier techs (Alpha, Math, Aesthetics, Code of Laws, and indirectly Currency) that define the following stage of the game.
-On the other hand, the only religious techs you should ever really pay attention to are the ones involving the Oracle, if you have a start and civ conducive to trying for it. If it looks like you can quickly build it (you have Marble nearby and start with Mining or Mysticism) or can power chop it (many forests), you'll need Priesthood to build it. Note you'll also want to have Bronze Working/Masonry as applicable and to get a worthwhile tech jump you have to have certain other researched already as prereqs--for instance, slingshotting Metal Casting requires you to have both Bronze Working and Pottery, going for Code of Laws means you have to have Writing (you'll have Priesthood already) done, etc.
-Just in general, as others have said, pay little heed to the science slider in favor of getting done what you need, which is namely settling a few good spots and improving resource tiles, connecting cities with roads, getting the important techs first etc.. It's a race to writing basically before you start major expansion, and then to Currency after you start to take land. You have an variety of ways to get there at this point (run scientists to generate beakers even at low slider, tech/trade Alpha to trade your way forward or build research directly) but it's important to reach Currency so you don't bog down entirely and never dig out.
-Currency is also a major, majorly important tech. As you expand, its array of ways to make gold help you fight maintenance as well as the free trade route in each city softens the blow of each additional site a tiny bit. Trading for lump sums of gold is great way to suddenly rush forward on a tech to complete it in a few turns instead of slowly (and less efficiently, look up binary research if you care to know why) over many. Selling off tech or resource deals for gold can keep you afloat, etc.
-Since Slavery is so powerful, Granaries are very useful for improving the output of your cites. With sufficient happiness, they allow you to create a burst of sustained production from the lesser turns waiting to grow back up.
-Forges likewise improve slavery even more, as the production bonus makes whips stronger for more overflow or easier to reach thresholds. Metal Casting is hard to trade for early from the AI, but you can Oracle it or even self-tech it after trading for Iron Working. Even if you pick it up later, you should immediately dump a forges into any city that you use to produce anything (so, like cities that only run specialists don't really need one).
-Most other buildings don't matter for a considerable amount of time. Granaries are always great except if you intentionally ignore Slavery or the city can't grow well anyway. Libraries are not exactly "spam everywhere" buildings but are integral to helping you along to Currency or grabbing some tech for trade. Forges are great in just about any city if you can get them. The last impactful one for quite a while (like, until Factories) is the Courthouse, but it's more situational as by the time you can build it, you should have several measures to help stay above your maintenance costs in various ways including simply building wealth or banking fail-gold into wonders, for those situations where you can't even trade for gold.
-Pick out a spot with high food, customize the tiles around that city to give as much surplus food as you can and use this as your primary Great Person generator. Running scientists everywhere with Libraries is fine for a while when trying to survive to Currency or just until you get your first 1-2 Great Scientists, but it's really much more effective to specialize one city to generate the bulk of your GP due to the way the mechanic behaves. Snag the National Epic here and leave production and commerce to your other cities.
-If you have crappy land, you'll pretty much have to pick on a neighbor and take some of his/hers. Early war isn't so bad so long as you can hit in numerical force before they get Longbows (Feudalism) and walls with a lot of culture defense, and you can pull it off with some easy to get units if the resources are favorable: Axes, Chariots, even Horse Archers (tech yourself) or Swordsmen (trade for IW, only tech yourself as a last resort). Some civs' unique units also work well. It's also relatively simple to set up too, just get Granaries+ Barracks in your cities, whip out a force and hit early, focusing on improving tiles for food/production over commerce and chop/whip liberally into units. After you take, focus on improving what you have now and use your conquest gold rewards to help fund your way towards the important techs you need normally.
-Just because I didn't state it before outright: don't fear whipping your cities! I know I didn't like to when I was new to this game. The production you get through Slavery is amazing (basically makes food = hammers) and if your cities have a good food resource or two they can grow back with little impact other than stacking unhappiness if you do it too often. You have limits imposed on your happy/health that limit much population growth for quite a while until you can start accessing more resources and better civics, so it's fine to keep your cities smaller and whip them to put that food that they otherwise don't need to good use, instead of being wasted stagnating or feeding citizens who cost more maintenance but do nothing. Not every whip has to be for maximum overflow or timed to never stack anger either; as long as you aren't 1 pop whipping every turn and leaving some recovery turns on your cities to stagger their anger penalties, it's manageable and still improves your overall productive output.