Some of the above is dependent on play style, but i will toss in my two bits.
Normal speed map:
Start game -> Ctr R and Look at resources
99% of the time have faith in the game and settle in place
I don't go for early wonders, so my tech path does not try to unlock them and build them.
If coastal start with 1+ ocean resource and fishing as starting tech build work boat.
Otherwise start worker, should have 12-15 turns to research something for him to do.
Ideally start with a farm resource and research agriculture.
I would probably give priority to the highest food resource in the capital. Usually it is agriculture, but animal husbandry and hunting can have good food specials.
If we can't get to that before the worker finishes, consider mining if there is a bare hill. If we can't reach any techs that let us improve a tile build a warrior instead of a worker first and b-line bronze working or animal husbandry.
After getting 1 resource tech i can bring online with the first worker. I usually get bronze working. Build warriors to 3 pop and improve 3 tiles (prefer resources then mines) with first worker and make a couple settlers. Chop if i feel like it. Usually switch to slavery after the second settler.
Food Techs: Agriculture, Fishing, Animal Husbandry, Hunting
So we have:
Food 1 (Highest Food Resource at capital) -> Bronze Working -> Food 2 (Animal Husbandry, reveal horses) -> Wheel (start hooking up resources/cities) -> Get any other techs for available food resources -> Mysticism (sometimes early sometime late, depends on if i need border pops early for fewer stronger cities)
If no military resources came up roll the dice again and try Iron Working. Also may get it early if there is a lot of jungle.
Second city should be up by the first or second miscellaneous food tech. Add a worker or two to the empire. Continue to expand (Normal map 6 cities minimum, 10 is plenty). My rule of thumb is Expand until the economy is in bad shape. If you can't expand build military units until the economy is in bad shape and then attack a non protective neighbor. On a normal map you want at least 6 good cities (minimum for national wonders). Ideally you will want a neighbor or two's capital to specialize a couple super cities.
On the way to the crash Tech:
Pottery (Granary/Cottages) -> Writing (Stop research and build libraries)
Stop research to build up some cash and to later run science at 100% through libraries. The crash is usually starting when libraries are finishing. Cottages can be build anytime after they are unlocked. I don't like them much, but prioritize getting them up and worked in your capital's riverside grassland tiles. If you want to become a cottage spammer, look for grassland heavy cities and cottage them up, but remember to have at least a 2-3 production cities (probably try to keep 50% production cities as you expand).
Once you have libraries online max the science slider and run science specialists as needed to get alphabet and currency. Emporer+ may change this tech order, but you can adapt to that when you get there.
Alphabet lets you build research, which is good early filler when you don't want to make anything in your cities. Currency lets you build wealth in your cities, and comes right after alphabet. Either one should help you tech through any crash. Wealth is good to build in some cities to run the science slider higher and i usually rotate a couple cities building wealth for a long time after the first crash.
I think i am at 10 techs
Trade bait is usually next (Aesthetics+Literature), trade for Iron Working and religious techs, then research Code of Law -> Civil Service, and Happy resource techs.