Eric,

The hardest part of learning to fly is paying for it. Before you pay for it, however, and before you take time off work, get your ground training and knowledge ("written") exam out of the way.

Three weeks is a tight time schedule to get the private done. The fastest I've had a student do it is one month; it can be hammered out, but there's something to be said for taking your time, and absorbing and internalizing what you're learning, as you go. I wouldn't rush it too much.

I'd also consider doing your training outside the Miami area; in congested areas, you'll spend valuable training, rental, and instructor time getting in and out of the controlled airspace, to an area where you can practice and train. You will be dollars ahead to train at a less congested location. While there's something to be said for exposure to busy locations, you can get that exposure later, after you're soloed.