My first choice would be the 308, it is like the 223 in that surplus ammo, as well as remanufactured (factory reloads) are available. It's nice to shoot for cheap. Also, compare the trajectories of a 55gr 223 to a 165gr 308. If memory serves me, they are VERY similar at least to 400 yds or so. For larger game, ie Elk or Moose, check out the Federal high energy with a 180 gr Nosler Partition, again a very similar trajectory. For a second barrel, my personal choice would be for something fun, a 357 or 22 hornet, but the hornet is probably not a great choice if you don't handload. 357 is available remanufactured also and quite inexpensive to shoot. Those would be my choices, but i haven't seen any bad advice on this post, so go with what YOU like.
DW