don't bother with wonders unless you've got really good production or stone hooked up to your city. if it says a wonder is going to take 100+ turns and you've already got a city or 4 or 5 then it's not worth it.
I disagree with this bit, Stonehenge is perhaps the most important wonder to build immidiately.
Give this a shot on the research front
1. Research Mining
2. Research Bronze Working
3. Research Mystic
Give this a shot on the build front
1. If city has access to something that gives extra food, build warrior first and grow to 2 ppl. If not build worker
2. Build / Chop 2 more workers
3. Chop Stonehenge. You will want to time the completion of your 3rd worker with the discover of Stonehenge
After that research Road and Pottery. After that, what ever you need, Agriculture, Fishing, etc etc
But Pottery and Stonehenge are critical, gives you free culture building and cottages for eco.
Oh, and 1 more thing, play at Marathon speed, this will teach you how to best use all the ages
No. There are precisely zero wonders that you can say are important before even starting the game. Some are favored on certain maps, but ultimately, zero.
Marathon drastically affects the game balance and once you're used to it invariably makes the game easier (since both you and the AI essentially get a free heroic epic or so in each city, but the AI keeps the same unit/building distribution it has on other speeds). That doesn't mean it isn't fun to play, but keep that in mind!
Really just reading war academy articles and walkthrough games over on strategy and tips are the fastest way to learn (for me this was settler---->immortal in less than a year, despite barely playing earlier civs).
Snaaty's guide to emperor+ can be applied to other difficulties as well although the early barb/ai defense that guide affords isn't truly needed until emperor...it will certainly work.
Generally speaking, rare is the opening where you wouldn't start with a worker, research to improve the specials in the capitol, and build some warrior/scouting units while the city grows. Make sure you prioritize working improved tiles.
Stonehenge is certainly useful but it's nothing a chopped or whipped monument can't mimic. Or religion. Or a caste artist...etc. Often the cost of the wonder makes it not worthwhile (going for it may cost a city spot, another wonder such as great wall, etc etc). This is true even at lower levels. At higher levels like emp+, going bronze/SH and not having copper readily available is a death wish unless you turn barbs off.