MD:
Good questions. We'll try to not steer you into the carbon fibre/titanium/etc toys that some of us spend too much money on.
If it is flat, you don't really need multi gears. Simplicity is good. It costs less, weighs less, and requires less maintenance. That said, a three speed internally geared hub is nice. They used to be made by Sturmey Archer, now there are multiple brands. If you have a derailleur, there is more to adjust/go out of adjustment. But more gears to pick from. Any chance you might want to use it up north in hill country as well? The less expensive derailleur bikes will tend to have a front triple (three chainrings on the crank). That gives you lots of gears, but is extra weight, and they don't shift as nicely. Triples are falling out of fashion, with front doubles with compact cranks (smaller chainrings) replacing them.
The style of bike you describe is often called a hybrid. Not a mountain bike. You don't want suspension for your use, for example, except in the seat. You will also see the label urban, or town bike. They will have an upright riding position, more of your weight distributed on the seat than the bars, good visibility.
Tire have gotten very fat (style/fad) but those are more expensive. Not necessary IMO. You just don't want any tire thinner than about a 28C. 25C at the minimum. 35C would be fine.
Frame size is dependent on a basic bike fit by a reasonable bike shop. There are no real standards. Probably around a 58 cm, but you have to try them out.
Weight doesn't matter unless it is ridiculously heavy, especially considering the flat terrain. Light costs money. That price range will have many options with aluminum frames, but it is the components that weigh the most.
Go with a name brand over a department store bike. Trek, Specialized, etc. That way you get to deal with an LBS (local bike store) and talk to a real person that can make sure you get the right bike. I think picking the right bike store is more important than the brand.
Something to check out is the trek bikes web site. Pick the bikes tab. Pick the fitness category. Look at the FX. Lots of choices, reasonable cost. An FX 7.0 is probably in the price range. Look at the Recreation category, where they have the Verve. The Urban category has the District and the Earl. Both have some style. I like the steel District a lot. Single front chainring, useful carrying capacity, disk brakes. Nice bike. Over your price target, but good value IMO.
I didn't go to the Specialized site, because I know Trek better. They will have similar products, though.
Think about how you will use it. Do you need a rack to carry your purchases? A secure lock?
I am thinking about another bike, an urban bike to go with my race bike and wet weather training bike. It would be very simple, and classic. It would have the ability to carry things, so I like the French Porteur style with more trail in the front fork. The leading candidate right now is the Felt York, with a two speed kick back hub (pedal back momentarily to shift high/low, no cables or shift control). Very cool bike. This is the Canadian site for it:
York - Felt Bicycles
Good luck, and ask away.
Jeff
Every time I see an adult on a bicycle, I no longer despair for the future of the human race. - H. G. Wells
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