Continents is my favorite and is probably the best learnig game. Invading another continent can be both fun and challenging with its own strategies and techniques.
On Civs:
There are a lot of civs that work well at AW and some that are not so good. It is a combination of UU and traits:
Traits:
Expansionist is the worst. You don't want to explore too much because early contact can be a killer. Only time it becomes strong is if you get a settler from a hut (at demigod, I believe the chances for a settler are 1/5, which is higher than at emporer and monarch due to an odd quirk on how huts work.
Religious isn't very useful. You tend not to switch governments often enough to make the short really worth while. Going to Monarchy and staying there is most common. Communism come late and takes too long to set up well. Corrupt towns are very useful in Monarchy as science farms (many scientists). Communism is will have more shields (once you have courthouses) but less science in general.
I think religion has a secondary benefit. Cheap temples means you can get culture expansions fairly easy. Also early temples allow you to better keep up in terms of culture, which in turn makes capturing cities more viable. I am personally a big fan of city capture. Getting a city of size over 1, usually with an aquaduct already, and not having to spend ones own population make them worthwhile. This is especially true if they are corrupt - you can immediately higher 2-4 scientists so capturing a civ of large cities can be worth 100 beakers a turn or more.
Seafaring is only strong in rare Archipellego AW.
Agricultural is one of the strongest traits (unless you are playing an archipelago with no rivers). Extra food is an obvious advantage. Cheaper aquaducts is also a big savings since towns over size 6 get extra unit support in Monarchy, you tend to want them early.
Military is also very strong - cheap barracks and walls (fast walls can really help with defense of new towns) Armies are key for AW so more Elite is very important.
The rest are good but not the best:
Commercial is nice because you do all your own research and need the cash.
For Scientific, Cheap libraries are nice for culture expansions and faster research.
Industrious is good - you set up your initial civ faster, and spend less gold on workers
Some good Civs:
Iroquois - Agricultural + commercial is very strong. UU: A speed 2 strength 3 unit for only 30 gold with HBR is pretty powerful.
Ottomans - Have a later UU so better golden age. Cavalry tend to be the unit where you start making real progress so the Sipahi are very nice. Industrial + Scientific is decent.
Romans - Militaristic + Commercial is very strong. Legions with defense 3 are more free to attack when it means being next to an enemy.
Germans - Scientific + Military is very strong. Their UU comes a bit late but is useful if you have a tough game that lasts that long.
Persia - Scientific + Industrious is decent. Having an early attack 4 unit is what makes them strong.
Celts - They have Agriculture which is strong + religious which is less so. Speed 2 swords is very useful (can attack and retreat) but because of the higher cost it is sometimes hard to get enough of them.
Greece - Great defenders. Cities with walls will hold off attackers even with knights and MDI. Science + commercial is decent.
Maya - Industrial + Agri is very strong. Their ability to generate slaves makes them able to spend gpt on workers. Javalins are not bad units.
Sumeria - The higher the difficulty level, the better this civ is. They are probably the only civ that can defend (for a while) vs SID. Early GA is a disadvantage, but can be used to pump out cheap Enkidu which can sit in mountains and hills and the AI can't send out workers to improve lands.
Agri+scientific is very strong as well.
China - Militaristic + Industrious is very strong. Early speed 3 Riders make great armies (Move 4 armies make a difference - that is 4 attacks per turn and can penetrate into enemy territory).
Aztecs - Mil + Agri is probably the best combo. Jaq warriors are less than stellar however. Doing a Jaguar rush on a nearby civ can be worthwhile.
I think this is a list of the traditional "best civs" for AW. There are other civs that I think are decent and some that are bad. Worth mentioning:
Spain with seafaring and religious has poor traits. Their UU has one huge advantage however. A Conquistador army can move and pillage 9 squares a turn. This is very powerful - make 2-3 of these armies and the AI will have unimproved lands. Their fast movement means they can catch workers and disband them - something other Armies have difficulty doing (speed 4 armies can do this sometimes).
India If you are feeling unlucky, being able to build knight like units without resources any resources is a big advantage (they get an extra hp as well according to civopedia - don't think I ever noticed that).
Best(from above): Iroquois, Ottomans, Roman, German, Persia, Celts, Greece, Mayans, Sumeria, China, Aztecs
Very good (nearly make best list):Japan(Mil + Def 4 'knights'), Dutch(agricultural + Def 4 'Pikes'), Viking (Militaristic, early attack 6 unit, 'best' if Archipelago), Spain (on standard or smaller map)
Good: Babylon, Byz (one of the best if Archipellago), Carthage (UU is a bit too expensive but a strong defender), France, Inca (agricultural), Korea(UU a bit late though), Mongols(only because Militaristic - exp trait and UU poor), Zulu (militaristic, UU can supress nearby worker action), India.
Fair: Egypt(bad if late contact and UU not used), England, Hittites(bad if UU not used), Portugal(assuming not Argipelago, bad for Pangea), Russia (multiple attack Cav UU might make it 'good' - not sure)
Bad: America, Arabia
A final note is that these are personal opinions. Different play style can change the list. For example, Japan is not "best" because I don't tend to use the defense of Knights very often when I play and Vikings aren't because Berserks are slow and I prefer faster units.