The "reaching" feel may just be a matter of getting used to bike riding. I think most people imagine they should be sitting on the saddle and holding the handlebars the way you might hold silverware at the dinner table. That's incorrect. Your weight should be supported by your hands, feet and sit bones, and to accomplish this you'll need to be leaning on the bars to some extent. If you try to avoid putting any weight on your hands, that will cause a sore butt (among other problems). Of course, if you put too much weight on your hands, that's bad too.

Sheldon Brown really is your second-best friend as a new cyclist.

Your best friend is the friendly worker at your LBS. They probably put their logo on your bike somewhere, which you should treat as an invitation to go back and ask for help whenever you need it. They may try to sell you things, but they'll also try to help.