As for packing up (since you only have two rooms), I’d recommend getting actual moving boxes. These are sized to pack completely into a truck. U-Haul has a fantastic supply of these, and a bunch of specialty ones (TVs, Lamp Boxes, Dish Barrels, etc).
As for how to get there: it’s a lousy time of year to drive across the US. If you’ve got the time, plot a scenic route and avoid pulling into urban areas at rush hour. If you don’t have the time: ship your car (or sell it and buy a replacement in FL).
If you’re moving for a job, are they offering M&L? If so, take advantage of that because the movers they recommend will be more interested in keeping the company’s business.
Can you share why?