I think anytime you make that first jump to a new difficulty level, you are going to be out of your element and struggling.
Try concentrating a little more on you military. Start a war with a nearby civ early (certainly before 1 AD, preferably earlier). Don't worry about wonders or buildings so much, just make sure you have a Granary and Barracks in your first few cities, and crank out an invasion force. A mix of Axemen and Swordsmen will do ok. Put a priority to researching Construction and getting catapults....though if you attack early enough you can take down a first rival civ without them.
Make sure your workers are building plenty of Cottage improvements along with some farms. Cottages are what produce your commerce; commerce is what gets pumped through your science/gold slider to produce your research. A citizen must work the Cottage tile to get the benefit from it. The more it is worked, the bigger it grows, eventually into a Town, which will give you a LOT of extra commerce. A city surrounded by Towns that are all being worked will generate a huge amount of commerce for you (and therefore a huge amount of science research if your slider is set appropriately).
