I've done a couple of 14'ers in CO, one as a day hike one as an overnight. The key is acclimatization, hydration, and listening to your body. There's really no way to tell beforehand how your body will adjust to altitude. Some people handle it without trouble, others will have headaches the whole time, others will get sick and have to head down. Fitness doesn't really enter into that part of things; altitude sickness is unpredictable like that.
I've been to 18,000 in Nepal and it was certainly slow going travel, but that was just a walk up. Glacier travel on Rainier is a whole different beast, with real danger from ice falls, crevasses, self-arrest, plus all the altitude problems. Once you gain experience it's something that you can do without a guide, but if this is your first time doing anything like this then a guiding service is really your best bet.