Thinking about buying a bike

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The wife and I have been thinking about buying bikes, sans motor, to cruise around town on. I'll admit that I'm fairly ignorant to the biking world though. I think a road bike would be best simply because we don't have a ton of terrain around us for trail riding. But I'm by no means opposed to getting a trail bike as well or possibly a hybrid if that's the best fit.

There is a new bike shop that opened just down the street from us, I think the best place to start would probably be to head in there to get measured for the right height but I'm not sure.

Any advice would be great because I flat out don't even know what to consider when I start looking. But in general my goal is to not do any of these things: