You have everything right there.
Buy the fittings you need from your local hardware store, and connect it to the capped end where it goes into your hot water heater.
Won't cost you more than 10 bucks.
Personally, I would put another shutoff valve coming right off the T before you hook up the burner.
That way you can cut pressure to unhook it for any reason.
You can also just bring in your hose, and shutoff valve to the hardware store and they'll give you the fittings to make it go together correctly.
Regulators made for propane will work with natural gas fine from a safety standpoint because NG runs at a lower pressure than propane.
Regulators made for natural gas shouldn't be used with propane because propane runs at a higher pressure than the NG regulator is made for.
NG regulators operate at a lower pressure than LP.
Some NG regulators have an overpressure lockout that will just not allow them to work if the pressure is too high.
Propane regulators can handle up to twice the pressure of NG is some instances.
So basically, either way your regulator will work just fine if you are using Natural Gas as your power source.
If you were converting from a NG regulator and going to propane, you would have to change your regulator.
Good Luck.
Tav