Pretty ambitious undertaking, especially for a first venture and not knowing "how to get from A to Z".
First consider that Tallahassee to Tetons, Yellowstone, Glacier, etc. and back home and taking in at least part of Rt 66 along the way you are looking something in the range of 6,000 miles. Assuming you take the full 6 weeks you are going to be averaging 1,000 miles per week, nearly 150 miles per day. Driving no more than 55 and you "prefer to stop, shop and Gaul to and from" you are going to be constantly on the move. You would not spend two nights in the same place very often.
Now can it be done? Certainly as long as you are prepared for the above.
I would recommend getting a book, or books, on Rt 66 and plan to limit it to the Oklahoma and Texas panhandle sections. Then you could turn north thru TX panhandle and northern NM to I-25 and north thru Colorado and into Wyoming and cut across to the Tetons, before continuing north to Yellowstone and Glacier and back home on a more northerly route as it may be getting hot in the south by the time you return in June.
A second person would sure be an advantage to share the driving as that will be one tiring trip.