Denali is a bit beyond my own personal limits. Admittedly, fatalities are down to 0.5%, but 25 years ago, when I considered it more actively, 600 people a year attempted, half succeeded and 1% ( 6 per year, on average) died in the attempt.
I've taken training courses from RMI and had instructors such as Nawang Gombu Sherpa (first human to summit Everest twice and Tensing Norgay's nephew) and Marty Hoey (who hoped to be the first American women to summit Everest but was the first American woman to die on Everest). I found their courses to be very well done and the skills I learned are still with me and maybe saved my life, or at least my legs, when I peeled off a steep slope of Pyramid Peak in Desolation Wilderness in winter. I was disappointed by their guided summit climb in that they turned us around prior to the hut, basically because it was going to be a slog and most tourist climbers don't like to climb in bad weather. But their skills courses are well done and especially once past their basic classes, you'd be well-served to learn cravasse rescue, high-angle ice travel, etc.
A friend from my Scout troop had a plan and followed through. He went into the Air Force, finished first in his class and got to pick his assignment. He picked SAR in Alaska and climbed Denali a few times while on leave. Once discharged, he started guiding professionally and mostly did winter trips. Colder weather, but more stable conditions. He said the hardest time he had wasn't any technical climb or rescue but trying to keep his clients sane while pinned down in a snow cave for 3 weeks. Last I heard, he, his wife and children lived in New Zealand we he lays brick, and he'd commute to Alaska each year for the climbing season.
http://www.everestnews.com/pak2005/martyk22005.htm
– get your snow and ice skills down to the point were they are instinctive as others have pointed out.
– learn how you react to altitude Do lots of 14ers, but get higher as well. The Mexican volcanos ought to be a cake walk for you before you try Denali unguided, IMO.
– learn how long it takes you to condition before a high summit attempt.
Denali is one of the four "tallest mountains on Earth". It's summit is the highest above its base AND its summit is climatically the highest (highest above local treeline). Everest is highest above local mean sea level. Chimborazo is furtherest from the center of the Earth (due to the equatorial bulge). Mauna Kea is highest from its base (below sea level) with 13,000 feet of dry mountain above 18,000 feet of submerged base. Everest is remote, with the thinnest air, and you need a visa. But Denali is not far behind in difficulty and risk.