I am wanting to add A/C and heat via a roof top unit.
The heating element of rooftop unit will not keep you warm. It'll take the morning chill our of the air on those brisk 50 degree mornings, but that's it. If you want to keep warm you'll need any of the following: idle the van all winter long, a sub-zero sleeping bag and a flight suit, or a your pal Mr Buddy propane heater, or an Espar heater - listed in descending order of preferability and efficiency.
I am looking for one simple definitive answer. What is the best way to power a roof top unit.
Shore power or a generator.
I would prefer to do it with batteries that could be charged by my existing alternator using an inverter. Is this possible?
Yes, it's possible. But it's impractical to the point where you should dismiss the notion immediately, if not sooner. To run any heat-resistive appliances (electric heater, air conditioner, etc.) off of batteries, you will need to make the decision to haul batteries or freight, because you won't have the weight capacity to do both. Even with a really efficient Coleman Polar Cub A/C unit, which draws between 1225 - 1450 Watts, at 120 volts AC that's 10.2 - 12.1 amps, let's call it 11.1 overall, and through an inverter that's 112.3 - 132.9 amps, and 122.1 overall.
That's an average of 122.1 amps an hour, every hour that it's running.
To run the A/C 8 hours down to 50% Depth of Discharge, you will need a battery bank with a minimum Ah capacity of 2400 amps.
A battery bank consisting of 6 pair of 6-volt L16 batteries gives you 2400 Ah. That's 12 batteries, each weighing in at 125 pounds, for a total weight of 1500 pounds, not including 100 pounds or so of cables and lugs. And, in order to put the used 1000 or so amp hours back into the batteries, you will need something other than your vehicle's alternator that will throw between 10 and 30 amps at the batteries. Using your vehicle's alternator it would take approximately 2.8 days of uninterrupted charging to get the batteries back to a full charge. With a dedicated
90 amp charger it would only take about 18 hours, though. But of course you'll need shore power to do that.
I'm worried about cost but only to a point. I'm willing to spend the money for a system that works. Is there one?
If weight and money is no object, $4800 for the 12 batteries, plus $300 in cables and $400 in lugs, another $100 for Class-T fuses and a busbar, and you're golden.
I realize I should research this and answer the question that way. Unfortunately I'm running out of time to attempt to gather the 50+ years of experience the folks on this website have under their belt. I need to get this done ASAP and I am running into crooks who are trying to take advantage of me. I would just like to be armed with some solid information while dealing with them.
ASAP means KISS, which means a generator, probably a portable one like the Honda, but full-size generators are also being used. It's what thousands (well, dozens, anyway) of van expediters use.
Another option for batteries, however, is a DC air conditioner, I think it's about $4500, and would only require 2 pair (4) batteries. But based on your post above, I don't think you know anywhere near enough about monitoring and maintaining such high dollar batteries for this to even be a consideration.
Batteries don't die, their owners kill them.