Just to get some clarification --
JaclynMcKewan, are you asking for top-end speed, or
acceleration?
If it's acceleration from a dead stop you want, then yes, a lighter bike will help. It will also help - somewhat - when climbing. But aerodynamics matter more once you're up to speed, and once you get past 25-30 mph, gearing comes into play, too.
Don't forget, though, that the bike is still a small part of the bike-and-rider (plus maybe cargo) package. But, you could say that a 20-lb bike can be loaded with 20 lbs of cargo before it feels as heavy as an unloaded 40-lb bike.
One more thing to consider about riding positions has nothing to do with speed or aerodynamics -- it's comfort. I got my wife a Townie earlier this year. It's a hoot to ride; it makes me feel like a kid again. You'd think that it would be as comfortable as sitting on a couch, which it is -- except that couches don't bounce up and down. Riding over bumps on the Townie puts more jolts straight up my spine than I get on my own "hunched-over" bikes. I would not want to ride that Townie over
maybe ten miles at the most, and although you said you're not planning to do more than 7-12 miles at a time, I'll bet that it won't be long until you're going out for 30 or more.