I would not recommend recommending a specific civilization just so you can win your first game. In my opinion, what's really great about FFH is the discovery of new mechanisms each and every game. Losing, winning, who cares?
So my advice is: pick the civilization you think looks or sounds cool. For instance, I'm sure you are already familiar with what elves are: dendrophiliac, long-eared crossdressers with longbows. If you like dendrophiliac long-eared crossdressers with longbows, then by all means start your next game as elves. They are quite different from other civilizations, but if you wanted to play as a "normal" civ, you would simply play BtS, right?
One advice in particular I think is terrible, is to take a barbarian civilization so that barbarians are not hostile. I think having to survive and fight the first couple of hundred turns through the hordes of barbarians is really, really fun. There could not be better motivation to understand the mechanisms of this new game you're discovering.
My first game I played the Amurites. I was actually disappointed because despite the raging barbarians option I did not really see any of them. This is because I started on a small island, easy to fogbust. Anyway, I had fun discovering the complexity of magic, for instance. Sure, I made a lot of silly mistakes such as not using religion at all. But I had fun anyway. Well, until I saw I could win and became bored with micromanagement and quit. My next game was also with Amurites, because I had learned so much in my previous game I wanted to try to put it into practise. I founded Runes of Kilmorph and I had great fun discovering how powerful religion was. Then I played as elves and had fun hugging trees. Then I played as elves again and was forced to start on a island with mostly desert tiles. This is GREAT: it gives you a really cool goal, namely terraform your island into a place suitable for dendrophiliac crossdressers.
To sum up. If your goal is to win, then sure, take a simpler civ. If your goal is to have fun, on the other hand, I would go as far as advising you to play your first game as: any civilization you think looks fun, monarch, raging barbarians, living world, more animals. Barbarian world if you want.
Of course if you never played vanilla or BtS that's a whole different story though.