How important is it to have "top of the line" gear? I am thinking that I'm going to see an improvement in comfort and shifting with almost anything at the "bottom of the line" for real road bikes (i.e. from a bike store not a box store).
I would generally agree with that. You're not going to get a $200 bike from a proper bike store, and for a road bike, you'll probably be looking at around $1000 out the door for something decent (and it will be radically better than your current bike).
Below a certain price point ($500-$600 for hybrid commuters, a bit higher for road bikes), components are chosen for cost, cost, and cost. Which, generally, leads to them being unreliable junk.
Once you hit that minimum price (and if you're shopping at an actual bike store, they usually don't sell anything below this price), you start having reasonable components that work well. They do what they're supposed to, reliably.
As you go up from there, to maybe 2-3x the base cost of a bike, things get nicer. The feel is better, the bike is stiffer, it's a bit lighter, and the benefits are significant for the added cost, though they may or may not be worth it for any given commute/use case.
Above that point, things start to get silly, and you're paying "more for less" - you pay a lot of money to get lighter wheels that are likely to be less robust for a commute, you get super light components, etc. Unless you are a sponsored racer, you don't need this, and more to the point, you don't *want* it for a commute - the weight reduction often makes things worse for daily riding in terms of long term reliability.
For a commute bike, you're right in that a base "bike store" road bike is a good spot to be. Depending on your weight, you may want to consider a heavy duty rear wheel or heavy duty spokes, and you may want to go with heavier/more robust tires and tubes for a commuter, but there's no reason to spend absurd amounts of money on something. You might want to go up a level or two from the very base model, but that's something that is best determined at a bike shop, test riding stuff.
Don't forget fenders and lights. :)