rjmarlatt, an F150 would be just fine for the application, lots of folks tow RPODs with them. The choice of 4x2 vs 4x4 depends on where you go and the time of year. If you found you used and needed the 4x4 capability of your present tow vehicle, stick with that. If not 4x2 will return a bit better fuel economy and cost less for maintenance in the long run.
RPODS are light enough that you have a broad range of TV choices, most vehicles with a tow rating of 5000 lbs or higher with a tow package and weight distribution hitch will work as long as you're not carrying lots of gear and people in the TV.
So consider what you want the tow vehicle to do for you when you're not towing. In the end, I chose a midsized SUV for my 179 TV because I no longer really need a pickup truck and find my Highlander more comfortable and useful the 90% of the time I don't have the RPOD back there.
Don't expect to get much better fuel economy towing with an SUV vs a recent vintage pickup. Assuming the tow vehicle has a modern efficient drivetrain the highway fuel economy is mostly going to be limited by the air drag of the trailer anyway. For reference, I get about 14mpg on flat ground, no wind, at 60 mph. I don't think its possible to do much better than that burning gasoline unless you drive slower.