Great job on your cycling!
It would take most people a long time to work up to 60 miles per week!
As far as what to drink. On the length of ride you do, I stick with water. When I do longer rides (20 miles plus) I tend to use dilluted gatorade and/or alternating water and gatorade. Drink before you are thirsty.
If you tend to "bonk" during your rides, suddenly running out of energy, then go with Gatorade, or another product (liquid, or energy bar etc) to give you the energy you need to keep going, but do it before the bonk.
To increase mileage, do it a little at a time. I like the earlier suggestion about a long day followed by a short day. I would go a long day at a leisurely pace, and then do the short day at a quicker pace. Vary your routine to influence different aspects of your fitness (endurance versus speed, fat burning versus aerobic/cardiac conditioning etc). This can also help to prevent boredom from setting in.
To increase mileage, do it in small amounts, I have read that increases should be in the 10% per week range. So you may want to look at something like: 16, 9, 16, 9, 16 which would give you a 10% increase from 12 miles per day... do it until comfortable, then take another step up. The distances don't have to be so symettrical, it just made my math easier.
For the rawness, it happens to everyone. When I get raw, I usually use a topical antibiotic and stay off of the bike for a day. If you haven't tried cycling shorts, they can make a difference in comfort level as well. I add the vote for bike fit, whether with a shop or not. I do my own adjusting, and would have probably gotten the right adjustment earlier, but I did learn that little differences in adjustment do matter to comfort.
Also, if you can find them in Florida, start working a few hills into your route when you feel the urge to step it up a notch... This will do a lot to help you.
Of course, all of this assumes that it is within the level of exercise your doctor has recommended.