Misfit: Here's a little scenario to cover your contact situation:
You are the England, with France, Germany & Rome as neighbors.
You've just discovered the other island with China, Korea and Japan.
It's the beginning of the Middle Ages and Germany got Monotheism as their age bonus tech. Accross the water, all the tribes are equal in tech and lacking currency to complete the Ancient Age. You sell currency to the richest AI (Japan), 2nd richest (Korea) & poorest (China). That will probably bankrupt them all. Now Korea is in the Middle Ages and gets Engineering as their bonus. Use all your cash to buy Engineering from Korea. Then you trade Engineering to Germany for Monotheism and sell it to France & Rome for all their cash. Now you turn around and sell Monotheism to Korea for all the money you gave for Engineering. Now you have tech parity with the world and all the money. It's probably best for you research Theology, since it's the least likely tech for the AI to go for.
A little later Korea gets Feudalism. You wait for them to sell it to Japan & China to reduce the cost. During that period Germany gets Invention. You can repeat the earlier process to acquire Invention, Feudalism & all the worlds gold, while researching Theology on your own. By doing this you remain the richest nation and at no less than parity with the tech leaders.
A little later (after swapping around Chemistry, Chivalry, your own research Theology & Education), Korea discovers Astronomy. Your research on Democracy is complete (hold on to this little monopoly). Germany discovers Metallurgy. You perform that same little bit of tech brokering with both islands. It's time to start looking at selling the contacts. Hopefully you've kept that original galley circling the other island and avoided barbarian galleys. Now is the time for him to earn all those turns of upkeep. Move him to near the Korean port nearest to your island. Once the first Korean caravel leaves port, you'll be able to calculate about when it's likely to reach your island (assuming caravels can make the trip) and when it will be time to sell the contact while they still have value.
With your extra cash and all those universities you've built (plus the wonders you got with your pre-builds), you should be first to the Industrial Age. Start research on Medicine (the cheapest tech). Hopefully you'll be able to trade the last required MA tech to Germany & Korea to obtain the other optional (Economics, Military Tradition & Navigation) techs. I try to have a pre-build ready for Smith's, the best wonder IMHO. You've now got the bargaining chip of Democracy to deal to Germany & Korea for their bonus techs (hopefully one is Steam Power). With your head start of Medicine, you should be first to Electricity & Scientific Method. That will provide you access the TOE tech slingshot and you should never trail in tech again.
This was a little long winded, but I hope I got the major points across.
A couple more little points, I'd like to toss out:
1. Your world map is very valuable, do not part with it unwisely, but once you do, sell it to everyone at the same time.
2. Once you get caravels, load one up with a pair of settlers and a defender and send them over to the other island. If an AI war breaks out, move your caravel to allow you to grab a city spot that becomes available when a couple of cities change hands (no more cultural expansion). Land the units, form a city, start a harbor (which you can soon cash rush) and fortify the defender. Send the caravel back for another settler & a pair of defenders. Repeat as new land becomes available. This is your beachhead for future conquest.
3. If you see the AI have a city razed in a really bad location, get a settler there fast. The AI has future vision and will know the someday, oil, coal or another valuable resource us going to appear there.