For portraits and a 'walking-around' lens, I'd go with the 18-105mm. I don't have that lens, but instead have a 16-85mm which I love dearly, both for vacations and portraits. If you plan on doing portraits, the next lens you should get is a fast one--f1.8, to make the background blur and your subject pop.
I have both a D5100 and a D90; my other two lenses are a 50mm f1.8 and an 18-250mm and even when I have the longer lens on the camera, I rarely go out past 150mm--but that said, it really depends on what interests you as a photographer. A friend of mine takes mainly wildlife; he has a 400mm and is lusting after a 600mm.