I do fine in BtS... What's the difference between commerce and gold?
I have a hard time reading those two parts of a sentence in one go. Commerce and Gold are exactly the same as in BtS!
A few other things I've noticed (I'm only a beginner too!):
a) You'll switch through improvements much more often. Keep forests early on and build lumbermills (Archery tech) for early 2/2 or 1/3 tiles. On hills, chop forests and place mines (same yield, but you get chopping hammers and mines get upgraded by a civic and an end-game tech). Workshops are worthless until Guilds (?) is researched, which is why non-hill tiles should keep their forests.
b) Trade is MUCH more important. You have much more routes than in BtS and many more buildings that increase the yield. Connect cities early and get those +route techs and +yield buildings. If the map is spread on several continents, Astronomy is a MUST.
c) Generating GP is much less a question of "getting enough GPP" than it is a question of getting pure GPP. If you're going for Altar (either as victory or just for the benefits), try getting some +Prophet GP Wonders in a dedicated city. Later in the game, I usually dedicate a few cities to Priest specialists, by spamming their Cross with farms, giving them several religions and place their temples for a Priest spot. I can not stress enough that 10 prophet GPP/turn is better than 10 prophet +1 merchant/engi/... point per turn. I'm pretty sure the game checks which GP you need and then gives you the other one against all odds.
d) Workers: You say you have 3-5 per city; that's way too much. Early on, I try to get 2 Workers in my capital (3 if elven/orc). By the time you produced your first settler and found your second city, sufficient tiles around your capital should be improved for its current size, so I usually send my workers along with the Settler and build a road on the way there: workers can do two steps, so they can land on the tile and quickly build a road and still keep up with your warrior escort.
Other than that: beelining is much more powerful in this game, because the tech tree is shorter and fatter. Pick one or two lines (Usually economy as one and your Civs favorite unit type as second) and stick to them.