It would be helpful for folks to put their cards on the table. Raqbal suggested people go both ways, as in, as many people move from drop bar road bikes to hybrids or flat bar road bikes as from hybrids to road bikes. But how old are the people moving towards flat bars?

As said before, hopefully OP will go to a bike shop and test ride different bikes and make up her own mind. We are just kibitzing.

I understand that this is a sore topic among those who love their hybrids and don't accept the notion of "moving up" to a road bike when the rider wants to either ride further or faster. (interesting, though, that this phenomenon doesn't appear to exist in the mountain biking community).

I posted this in another thread a few weeks back, so take it FWIW.
The reason a few of us suggest OP just start with a road bike is, many folks take the below path.
1. Cycling newbie walks into a bike shop looking to do a little riding, nothing crazy mind you, just a few times per week, maybe the occasional MUP, dirt or gravel trail. Not being an experienced cyclist, she gravitates to some sort of hybrid, which looks like a nice compromise between the serious road machines, and the super slow cruisers.
2. After a few months of riding her hybrid, cycling newbie is back at the bike shop, or bike forums, looking for ways to make her hybrid faster and more road worthy. Turns out she really likes road cycling and doesn't ride unpaved trails nearly as much as she thought she would, but her $500 Trek FX, Specialized Sirrus, Giant Escape, Cannondale Quick is just too upright, perhaps she is riding with a club or group of road riders, or now wants to consider competing in a triathlon and now realizes she should have gone with a road bike.
2a. Friendly bike shop employee/bike forum poster suggests swapping tires for something narrower that can take higher pressure, swapping/flipping the stem to get handlebars lower, and adding bar ends.
3. A few months, to a year later, newly minted cycling enthusiast is back at the bike shop shopping for a road bike, which is (maybe) what she should have bought in the first place. If she has room, the hybrid is now relegated to the garage as a spare bike, and if she does not, it is sold or traded in at a loss. Good deal for the bargain hunter or flipper.

Now, I know this doesn't always happen, but it happens enough to at least go into this with your eyes open. This only matters to OP if she wants to do longer distances (40 miles or longer) or possibly, competition. 35 miles or less and you will do just fine on most road oriented hybrids.