Once I know what the race and class lim,its are for the game, then I tend to start thinking about what class I want. Race comes next an as I pick stats and skills, the character starts developing in my mind. Since at least 2nd Ed, I've always kept bonuses in mind. I mean, if you could play a Minotaur Fighter in 2E and yr DM gave 1 auto-18 to you, it was a no brainer to go w/a 20 strength. Halflings slaughtered everyone else at Thief skills, etc.
Even in 1 shots I'll usually still tend to optimize, b/c that is part of how I have my fun. If I do go off-type, I tend to correct w/feats and power selection to make up for the difference. Since the addition of the flexible stats in 4E, the options you have available are a lot better. I mean sure, you might pick a race that doesn't' have a bonus to his main stat, but you can throw an 18 there and look, he got a +2 to both his secondary and tertiary stats. That is never a bad thing.
Really off-type stuff is usually more of a 1 shot kind of thing for me. I roll really poorly, so not optimizing really hurts

If I'm going to play something like a Goliath Psion w/no stat bonuses to anything used by the class, I either would a)play something else or b)only do so for a very short game.
As far as halfling barbarians go, they actually make pretty good barbarians. Charisma and dex are both useful stats and the feat support halflings have is great. Very defensively minded, which lets you just wade right in. I'm playing a Halfling Daggermaster Rogue and even tho he's an Artful Dodger, my DM says I play him like a Brutal Rogue instead. He just doesn't consider other that much of a threat to him generally and he's a bit of a loose cannon, charging across the battle field and all. Loads of fun.