Dan is absolutely correct.
Freighters are operated to the same standards as any other commercial aircraft and just because they park in the rough end of the airport does not mean that they fly any differently to the jets parked on the air bridges.
Freighters are moving away from the 747 Classic/707/DC8 type operations, in Europe at least onto 744/748/777 equipment so experience of one of these types is an advantage. That means flying pax variants for a bit in practical terms. Some airlines operate pax and freight variants but the trend, again in Europe, is for freight to be carried by specialist operators, sometimes in the airline's colours.
As you are in the US, your dream ticket would probably be FedEx or UPS or Atlas who seem to be the big players. As has been suggested, with zero hours you will need to work your way up the ladder. Maybe consider a move to Florida. MIA and MCO are chock full of freighters.
Best of luck. I moved to freight a couple of years ago and the only question in my mind is why I didn't do it 10 years earlier.