There are several different systems. I like my Schneider XW-Pro unit, but the software has a few odd issues that I hope they will eventually fix. It can supply 6,800 watts. It can accept up to 6,800 watts of AC coupled solar. To add DC solar, you would need to get a separate DC charge controller. I only have my Enphase AC coupled micro inverters. My system is not off grid.
If I was building from scratch again, I think I would use an Outback Skybox as the main battery inverter. Then you need a 48 volt battery bank of about 400 amp hours for a typical house. Have you estimated your power needs? The skybox can provide 5,000 watts of power from the batteries. It outputs 120/240 split phase power. It can handle up to about 7,000 watts of grid tie type solar inverters on it's output. So while the sun is shining, you could pull over 10,000 watts. The Skybox also includes an MPPT DC solar input that will accept solar panels directly to charge the batteries. The DC solar input is a high voltage string, 200 to 600 volts, so that does need at least 6 panels in series to work well. You can find over 350 watt panels now, for under $200 each. For the AC coupled solar, I think it is hard to beat Enphase micros. I have 16 of their iQ7's on 300 watt panels. The 7A version will take up to 450 watt panels. With Enphase, they have a combiner bow where you can bring in up to four 20 amp strings of micros. I only have 16 300 watt panels, so it is just one 20 amp string. The combiner has the Envoy monitoring hub in it. It is how the system reports the production and also handles software updates and configuration. It should have an internet connection. It can do WiFi or ethernet cable. They also have a cellular option, but then you have to pay for a service plan for it.
There is also the Sol-Ark which is higher power, but cost a bit more. From what I can tell, it requires some DC coupled solar before it will use micro inverters. They have an 8,000 watt or a 12,000 watt.
If you want to truly run off grid(ish) you may need a bigger inverter, or stack 2. But most of us that do have grid access find it is cheaper to use the grid for heavy loads like whole house air conditioning, an electric clothes dryer, or if you have a welder. So I run 2 breaker panels. One is just on the grid, and the other is on the battery inverter. When there is a power failure, the stuff in the grid panel does stop working. But I still have the essentials. The batteries and large inverter and huge number of soral panels needed for me to go off grid is just more expensive than buying a bit of electricity for the heavy short term loads. My electric bills average about $50 now. Last month was just $35 and the summer with A/C on all the time just topped $130. Before solar, I was topping $300 a month all summer. The biggest cost is the battery bank. My system is using rejected Chevy Bolt batteries. They were new, but didn't meet GM's specs. I got 18 KWH of battery for only $2,000 but I had to build the system. The fuses, buss bars, cables, disconnect switch, steel cabinet, etc. probably added up another $1,000 by the time it was ready to run. And it has no warranty at all. I figure by the time the cells croak, there might be better tech available. 18 KWH of battery, is a little more than a Tesla Powerwall2. It's not quite enough battery for off grid, I save about 40% capacity incase of a power outage overnight, so by 10 PM I am back on grid until I have sun the next day at 7:30 am. There are companies that pre build battery bank systems. Many have been doing lead acid based battery banks for years, and they are still cost effective, but lithium is coming down in price, and they last longer and don't need constant maintenance.
All of the decent battery inverters that can run off grid will be able to trigger a generator start. This could be programmed to trigger a relay to connect the grid instead of starting a generator. Set it to cut in at a safe low battery level. With a little logic, it could still start a generator if the grid is also down. In a system like mine, I don't bother doing this as I have the grid connected all the time and just pull or export power as needed. And then the unit will isolate from the grid and run off grid only when the grid fails.
I think I hit all your questions. Don't be afraid to ask questions. The more you know, the better you can make decisions. Building a large solar power system is a big expense, so figure out what you want up front. In my case, I put in the Enphase solar first. I knew it would not provide power in a blackout, but I wanted to get the major expense in when I could still get the federal 30% tax credit. I think it is down to 15% or even 10% now, but it still helps. It was going to go away completely, but that may change now. Enphase did come out with their own battery backup system, but it is expensive.