So, I'm pretty new to Civ 5 too, and played at prince and am only now getting into king. I find playing on a few different map types to be the best thing.
I maybe too much of a newbie to pontificate on things like this, but Civ isn't really a game that is tailored towards a single map or game-type. To make a comparison to another game I'm sure most of you are somewhat familiar with, League of Legends is balanced around it's 5v5 map. While there is a 3v3 one, the balance isn't there.
With Civ you can play on any map, with any settings, and still have fun. You may have certain advantages or disadvantages playing on different map types, like Dido on a water map or the Inca in an earlier planet age, but besides that what you're doing changes little. The fun comes from making macro-strategic decisions while doing micro-empire managing.
So, personally, I like random map type or just manually switching it each game. I like to see what new terrain offers me, and get accustomed to adapting to it.
The simplest answer is - play everything.
As to what you should start with, pangaea is good because you meet all the civs early, it's easy to war if you feel like doing that and you can still go for peaceful strategies too. Continents is also pretty fun, though personally I find war a little bit more difficult and I'm usually the target of the warmongers on my side of the map, so peace isn't easy either.
And just play whatever civ catches your eye. My first was Rome, followed by Arabia, but you can pick any of them, or all of them!