Looks like lots of good advice in here on the bike and all of it useful. I don't recall seeing you say exactly what your current beater bike is so kind of hard to tell whether it's worth sinking a lot of money into but hey, if it's getting you there and back ride it into the ground.
The bike Chipcom suggested is a great baseline in terms of what you should be looking for if you're going to buy one and at what price.
The other suggestions I would add have to do with sustaining your energy and your body for these commutes. If you're riding in Florida (really anywhere) but you get little relief from the sun down there so make sure you're staying hydrated on your ride in and home. You might want to store some kind of energy replacement drink or fruit juices at your workplace. Bananas, Power and Clif bars etc are good to have not only on the ride but in your desk or briefcase at work. I've had long commutes and nothing is worse than simply bonking in the middle of the day when you've got a ton of work to do. If your job is very physical you'll need to watch your nutrition and hydration even more carefully.
I'd get rid of the backpack and go with a rack. Keep in mind that you are repeating the same physical demands daily so reducing stresses to areas of the body like the back, the knees, wrists, neck, shoulders are important so you don't end up doing damage to your body instead of strengthening it.
Cycling gloves will reduce fatigue and damage to your tendons and nerves in the wrist and arms and they are great to have if you fall or crash. Bars that allow you to vary your positions will also reduce fatigue. Make sure whichever bike you ride is adjusted properly and get rid of those plastic pedals and wear good shoes so that your foot is securely placed on the pedal. At those distances you may ultimately be a candidate for a clipless pedal or a pedal like the Campus pedal from Performance Bike that is clipless one side and bear trap the other.
It's a very doable commute and should be an enjoyable one- have a blast.