Go for foxes for fur. There's a specific fox trap for them which works very well. Fox furs are the most valuable to foreign traders. Though if you're going for luxury then hunt whatever seems most luxurious to you!
Don't build spike pits. They cost more lumber and they usually kill. This means if you fall in, it's big trouble, and if the animal falls in, the corpse may disappear before you can harvest it. Regular pits keep the meat fresh longer and you get a sprained ankle at worst if you fall in. It's also good for foreign traders, if you have trouble finding them to trade with, you can check your pits. Chances are there will be one loitering at the bottom, still willing to trade! Leave him there long enough and he'll manage to escape. That's in case you're going a slightly-more-legit route on trade. I capture and kill traders, myself.
Minecraft isn't survival at all, really. It was out for years before Notch was like, "Oh, right, hunger bar..." Best equivalent is the ... The mod I cannot for the life of me think of the name of. Terra-Firma Craft! Thank you Firefox download history. It adds quite a bit more 'effort' to things, but once you get settled in it's still pretty easy.