IMHO the Windsor Tourist is is a fine bike for randonneuring. Some might argue it's heavier than necessary and it's certainly not built up with uber-lightweight, stratospheric quality-spec equipment - but none of that is anything that is truly rhetorically valuable. It's a well-built bike - at least mine has been. I've probably got 4k miles on it and never doubted its "ability to finish" any ride. Others have gone cross-country on one without problems.
The only mods that I'd consider "out of the box" might be putting a mountain biking triple on the front - depends on your local terrain, the condition of your knees and any non-local terrain you intend to ride in the foreseeable future.
As far as "training to do randonneuring" goes, it kinda depends on your goals, but basically, I think "just ride" is the best advice. "Listen to your body" is the second best advice I've been given. Learn what a "recovery ride" pace is - use it. Recovery is as important for long distance riding as interval rides are.
Vary the rides in terms of terrain, riding/weather conditions, toss in a few short-distance "intervals" periodically just to vary things a bit, and learn about what clothing to wear when. I know of a few locals who don't ride farther than 40 milers as training for their brevets. If speed/finishing fast is your goal, up the number and intensity of the intervals. If finishing is the goal, then endurance is what I'd concentrate on.
The one thing that is relatively simple to do if you're planning oriented is to do a quick Net search for century-ride training programs and follow one of those ---- they vary in length from 8 weeks to 20 weeks. From that point on, you'll have a good idea how to proceed to brevet-length rides.
Edited to add: Find a decent handlebar bag and/or a lightweight rear rack and bag for tools, food and other gear you might carry. Some like the handlebar bag for its easy access while riding. OThers prefer the rear rack bag for its capacity.
Last edited by 20_700c; 10-18-12 at 06:41 PM.