The line that everyone played after 1.e4 e5 2.f4 exf4 for many years was 3.Nf3, but 3.Bc4 has gotten a lot of attention in the last fifteen years or so.
There was this game in 3.Nf3 that might be worth looking at:
http://www.365chess.com/view_game.php?g=361119
As far as your choice of opening goes, you aren't a professional player, so just play what you enjoy and experiment. It'll take you some time to get a feel for things, but be bold!
In the Falkbeer, the old line was 3.exd5 e4, but look at 3....c6 too. A lot of players use this to get to a variation of the KGA after 4.Nc3 exf4.