I've seen a couple combination charger/inverters too and decided on separates so if one dies, I only have to mess with it. I kind of also decided 800-1000 watts inverter or 3000 watts inverter are the sweet spots. I don't use AC or microwave dry camping, just the two 12 volt fantastic vents which move a lot of air and make hot days comfortable. All we need are computers, cameras, small devices so 800-1000 will fulfill our needs. If you want to run the AC or micro, hair dryer, coffee maker, etc... then get the 3000 watt inverter. A 2000 watt in my opinion falls into the too much, too little gap. Get a 1500 watt model if you're going to run power tools. I use battery powered tools so the 800-1000 watt model again will easily charge the batteries. A 3000 watt inverter means you will need about 4 group 31 or Trojan 125 or 105 batteries to support the current demand. I would also get a pure sine wave model.
That's my answer and I sticking to it.