I would highly recommend carrying your water in the integrated bladder, even though it's a little weird then sucking water out of the drink tube when you're not wearing it. Everything will fit better and bounce less.
I would guess that the Intensity vest would hold what you need, depending on how bulky your lunch sack is. Sounds about like what I take when I run to yoga. If your lunch bag won't go inside, it might fit under the external compression cord. If there's an REI or another Nathan dealer near you, you might want to see if you can take a look at the vests before buying.
Speed comes from what you put behind you. - Judi Ketteler