Depends on the inverter wattage. 200AH of good quality lithium should be able to power a 2000 watt inverter. For example, many of the portable power stations have less than 200AH and run 2000W inverters. With a 3000W inverter, you are likely pushing the limits, though.
Correct wire sizing and good connections from the battery to the inverter are critical. Usually, this is where people make mistakes by under-sizing the cables or doing a poor job on the connections. and cause too much voltage drop making the inverter go into low voltage shutdown when powering heavy loads.
It's always nice to have more battery capacity. :) Solar sizing is going to depend on how much energy you use each day that needs to be replentished. Everyone is different depending on their off-grid lifestyle.

Thanks, Ray. You probably hit it on the head. My inverter is 3000 watts. More batteries it will be. I used your videos to make my own cables, so I'm sure they're fine!

If I might add, there are two good Facebook groups that have helped with my education on solar.
Solar Powered Rvs and Boondocking and DIY Solar Systems.

I used two flood acid 6 volt batteries with a 2500 watt inverter and 400 watts of solar powering the complete trailer for 5 months in an Arizona winter. It all depends on what you want to run. My largest draw was making coffee in the morning (1000 watts) when the batteries were at their lowest. We could watch the 32 inch tv using our satellite receiver and my laptop every evening for several hours. If my batteries were down to 70% in the morning It was always touch and go not to have the inverter trip out on low voltage when making coffee. If I had two 100 amp lithium batteries at that time there would have been no concerns at all. It all depends on what you want to run.