Give some thoughts to what you and your passengers, if any, want to do and see. This will in some ways determine when and where you need to be in Alaska to accomplish your goals. If your main interest is to photograph wildlife, especially new borns, then plan to be there in early summer, at some of the known good locations, such as the Chena Hot Springs road, the Alaska hwy area south of Watson Lake are just two of the many places i think of for this activity.
If you are planning to fish for salmon, then you have to be where the runs are in progress. Check something like the
www.alaskaoutdoorjournal.com to see when the historic fish runs have occurred. They don't tend to vary too much from year to year.
Probably the majority of travelers go north on the Alaska hwy and then many of them return south on the Cassiar hwy. Some use the Alaska marine ferry system for part of one leg north or south. About the only way to see SE Alaska and coastal western Canada is by boat, ferry or cruise ship.
From south Florida, i figure about 10 driving days to Fairbanks and the same returning. However, we seldom drive straight through but will stop here and there for a few days and make it a two or three week trip to and from. Most trips we don't stop much on the way up or back in the lower 48 but keep a list of the places we wish to return and visit on a different trip.
Consider your age and health, as it can determine if one trip is all that is in your future or will there be multiple ones. It can be the trip of a lifetime for most, one that you can do over and over again. The far north country is so huge, there is no way to see it all in one lifetime, I have concluded. I tried for 25+ years to see it all and it just wasn't possible for me to do. Did my best to wear out 5 airplanes, a half dozen RVs and several boats but never saw over 3/4 of Alaska I would guess. Much of that was from the air at 3,000 to 10,000 feet. LOL
A new traveler, needs to decide what they want to see and do. This is often influenced by where you live or have lived. I notice people from the Pacific Northwest aren't as impressed with the mountains and water as I am, having grown up is southern Oklahoma. Have several priorities in your plans. If you are mainly going for the scenic photography and you hit a rainy summer like this past one, 2014, then you may have to fall back to doing more fishing, indoor type stuff, hiking in the rain and figure you will return again to do the outdoor photography, when the sun is shinning more. Or check the weather and go to a different part of the state or territory where the weather is more to your liking. Be flexible, I guess, is what I am trying to say.