While we're on American shopping turf, let's check out tee shirt options. Clicking on any of these images will take you to the Chadwicks.com page for more details.
Big scoops and gapey sleeves are in. Modest tees are hard to find. Here are two knit tops (above and below) that could solve those problems for you. Wear one on its own, or as an underlayer for those gapey-drapey items.
Here's another tee option (below). A bit more scoop to the neck and a bit less fabric in the sleeves, but the zoom feature seems to indicate that the fabric is opaque.
My motto is never trust a tee shirt until you've tried it on. The same goes for cotton button-up shirts, because fabric is often more transparent in reality than it appears in photographs. This is one of the hazards of shopping online, but posting back an unsuitable tee shirt may cost less than it would for you to drive to the store, try the garment on, and drive home again.
Keeping that in mind...
...this appears to be a cute basic shirt for a modest lady, provided you can remedy the missing buttons. If you're not wearing hipster skirt/trousers, you may get away without one at the bottom of the placket, but you'll almost certainly need more closure at the top. The following posts from August 2008 suggest options for that.
The Great Shirt Hunt, part 1