I fly a fair bit for work. I have the hang of it and am getting paid for it, but it is a bit of a pain, especially if you haven't flown in a while and are unsure about what all
the restrictions are and about the
3-1-1 bags for carry-on toiletries. Those are the two big things I see delaying others--and me if I'm behind them--in the security line. Since I fly frequently I have slip-off shoes, a
velcro belt (no metal) and a pouch in which I carry everything I need to take off for the metal detector to get through more quickly. (But keep your boarding pass on your person as you go through the metal detector.) And you really need to get to the airport 2 hours before the flight leaves to leave time for bag check and security check.
As for driving, that's a long drive, but if you have the time it could be a fun trip. For a single guy I find flying can often be cheaper than driving. With two or more obviously there's a scale of economy in driving.
I can't think of an advantage to renting and driving unless you have an older car you don't quite trust or need a minivan or passenger van to carry the people. But minivans run quite a bit higher than mid-size rentals, and Passenger vans run more. You can rent a travel van with all the luxury, but damn it's expensive. Last I checked--several years ago--they ran $900 + per week.
The train could be really cool, but it may take much longer to get there than you think. Last I checked--6 years ago--to get from DFW to Indianapolis would've taken a couple of days due to a 12-hour layover in Chicago. <checking web page> ... Actually it doesn't look as bad now, and there appear to be decent routes from Oakland to St. Louis and a bit of an out-of-the-way route from Los Angeles to St. Louis. Looks like you can get there in 2-3 days by train for under $200 per person (oops..that was the one-way price).
May? Planning ahead, are we?
EDIT: Hmm, I have some time off and no plans. I might check out a train trip somewhere just for the experience.
EDIT 2: I was imagining train travel with small cabins, but apparently the normal seating is more like an airliner or bus. The rooms cost $270 - $500 above the seat pricing for a DFW - El Paso trip. I'm not sure how the coach seat sizing compares with a plane or bus, but the photo makes them look big.