To echo the viewpoints of Bob, Josh and Steven, I would strongly urge you to pursue this opportunity! You are at an age when such an undertaking is far less difficult to take the time off than when you get older, entrenched in a career, have a mortgage and a family.
I have done but one long-distance trail, and did so at age 38. Except for the financial component, I can say unequivocally it is MUCH easier for someone in their early to mid 20s to undertake such a journey (wish I had known about the greatest of backpacking then). Obligations sneak up on you really fast in life, so to take six months off from my job (without quitting) required a very gracious and generous employer, an equally patient and understanding girlfriend, and tremendous support of my family, friends and coworkers. On the PCT at least, most of the people undertaking it are between 22-28 years old, with the next largest demographic being those 50 and over. There were relatively few people in their 30s and 40s hiking the trail, although during the recession there were probably a few more than usual.
So, if you have an inkling, do it! I think taking a guided trip is a good idea. Just getting some backpacking experience is very, very helpful. I knew people on the PCT who were making it their very first backpacking trip. Certainly, you can do it this way, but dang, I wouldn't recommend it. There is little substitute for experience - figuring out your gear and what works and what doesn't is something everyone must learn - by taking a few short trips before embarking on a 2,100 mile hike you can eliminate some of the stress and worry that comes with such a huge undertaking. Generally, new backpackers bring way too much gear. And the gear they bring is generally bulletproof, and therefore, heavy within its class.
It sounds like you are in great shape - that will help. I would say more that as important as being in good physical shape is to have a good attitude (your enthusiasm is a good sign!). Many people were surprised when they become discouraged at times on the trail - I think if you go in with the attitude that it's going to be fabulous all the time, well, you are setting yourself up for disappointment. Any adventure that lasts upwards of six months is going to be a lot like life itself - many good days, some great days a few poor days and some really boring ones. And frankly, what adventure story is worth reading that doesn't involve some hardships and personal trials? That is why they call it adventure. Nobody writes adventure stories centered around time spent at a beach resort in Cancun.
I would also encourage you to read as much as possible beforehand (as you've done), as this will undoubtedly leave you better prepared. One such book I can recommend was written by a fellow thru-hiker - one Bill "Skywalker" Walker/ I met Skywalker (that's his trail name) on the PCT after he'd hiked the AT. The guy is just a hair under seven feet tall and describes himself as the "world's worst hiker" which he was not. However he wrote a funny narrative of his time on the AT, "Skywalker: Close Encounters on the Appalachian Trail" which really captures the highs and lows of such a journey.
Regarding the "dangers" of thru-hiking, I think most are exaggerated. Certainly, there are bears. And snakes. And really bad weather. But the likelihood of being attacked by an animal is incredibly rare - among long-distance hikers the danger posed from a bear attack would be much greater in my estimation upon the far-northern reaches of the Continental Divide Trail, where there are grizzlies. But even then the chances would be quite remote. On the CDT and AT, I'd fear being caught in a lightning storm atop an exposed ridge line more than than I would a bear attack, for instance.
The biggest threat will likely be from injury. Among leading causes of death among backpackers/hikers, the leading two are falls and drowning, if memory serves correct. And most of those stem from poor decisions. Yet, on long-distance hikes, many people drop out because of injury, many of them related to repetitive stress. Finishing a long distance hike is as much a matter of tenacity as it is luck. Minimizing your pack weight (and the things within the pack) is key to reducing stress on your joints.
Finally, I would argue that it is the responsibility of every hiker who attempts such a journey to consider the feelings and fears of their friends and families. You need to do your best to educate and assuage those fears. People who don't understand will immediately think the worst will happen. Remember, the hard part is being left at home, looking at the weather and seeing heavy rain forecast and wondering if the person hiking is okay.
You could get a documentary like "Appalachian Impressions" by Mark Flagler which provides a nice overview of the trail,and invite friends and family to watch it. I think these documentaries do a great job of illustrating the allure of long-distance hiking and the unique opportunity that a thru-hike represents.
My friends and family were involved in my hike. They sent food drop boxes to post offices along the trail. I did meet them a couple of times at towns along the trail, taking a day or two off to catch up and enjoy each other. I did hike with my sister and brother for a few days (although honestly, this is difficult because you will be in fantastic hiking shape and will therefore, be so much faster than others). But keeping them involved and informed of my progress helped them as much as it helped me!
Take care and go for it!