Hello and welcome to the RTA forums !

The weather really is totally unpredictable at the exact time you travel and so far ahead, but travelling in the middle of winter means you have a higher risk of getting travel disruption from Storms, wind, snow and ice. With fair weather you could drive the route in 6 days at a pretty brisk pace so you need to decide how much time and money you can spare for sight seeing along the way. A lot of natural wonders will have limited access, especially around the mountains if you are interested in anything other than the Cities you have listed. Is there any way you could take the trip later in the year ? I think it would be less risky and more beneficial to travel in the Spring, the later in the Spring the better.

You don't say how many people are travelling so recommending which class of car to hire is difficult, other than to say a Mid-size sedan can offer a good combination of comfort, economy, size and competitve rental fees. Now you have an outline of the route you want to take you should get some good paper maps and use RTA as a research centre where you will find lots of info by diigging around and using the search function. With around 3 weeks to travel you have time to spare, but where and how you spend it really comes down to your interests. The advantage of travelling this time of year is you will have little problem finding a room for the night and you could just 'wing it' and see where the road takes you. If you are planning New years eve in NY, it might be wise to book up well in advance though. Once you have a few ideas and/or specific questions, we can help fill in the blanks and answer them.