About a year ago I went through the exercise of solar and battery backup vs a generator for our new house currently under construction. First you have to realize that the most common type of inverter used for solar DC to AC conversion is micro inverters for many reasons too involved for this discussion. The problem with micro inverters is that they sync to the utility line frequency and when utility power drops, they stop functioning. So, to have solar with backup capability you have to have a stand alone inverter that can also sync with utility power but will function in a stand alone mode when utility power drops. In order to size that inverter, you have to know what the total load will be. Then you will probably find out that you cannot run everything on the house on any reasonably sized and priced inverter. You will be faced with internal house wiring changes, a transfer switch, and a safety outside disconnect switch to prevent electrocuting firemen if they respond to a house fire. In my new house I will have two load centers, one only for utility power and the other for backup power through a transfer switch.
Once you determine the total load you will run off the backup, you will have to figure out both peak and average load. The peak load will determine the size of the inverter and the average load will determine battery size depending on how long you want to run. The common metric is KWH (kilowatt hours) a measure of stored energy. For example, let’s say your average load will be 5 KW and you want to run for 48 hours. Not counting on significant solar contribution because you might have an outage in the middle of a period where a storm blocks the sun for 48 hours, you would need 5 X 48 = 240 KWH worth of battery storage. Then you have to account for that by the efficiency of the inverter. Even assuming a very efficient inverter you should plan on 90%. Therefore, the KWH you need would be 240/.9 = 267 KWH rounded off to around 275 allowing for wiring and other losses. Then figure out the cost of lithium batteries to provide that amount of storage. A 12 volt 100 AH deep cycle lithium battery will cost between $750 to $1,000. Each one provides at maximum 1.2 KWH assuming 100% efficiency which will probably be 80% at high discharge rates and allowing for safety to battery life by over discharge. So, the battery would provide 1KWH of usable energy. To get the storage you need, the battery cost would be at minimum $75 X 267 or over $200K. The batteries would also need a storage space and maintenance. Obviously, the scenario of 2 days at 5KW does not make any sense from a battery backup scenario. Even if you only wanted to run for 5 hours, you would still need in excess of $20K worth of batteries. It would be cheaper if you used SLA (sealed lead acid) batteries but their life is much shorter and the % or rated AH capacity at high loads drops more than lithium. And we did not take into account the inverter cost.
Looking at a propane fired generator, the costs are much different. First, I would recommend a propane generator instead of gasoline because propane does not need treatment or refreshing like gasoline. Second, your propane tank can serve double duty if you have an outdoor gas grill. No more lugging tanks to Lowes for exchange.
Looking at a reasonable generator that is 10KW, allowing many more loads to function, the price of the generator with a 16 circuit load center/transfer switch is around $3,000. That generator at 50% load uses about 1 gallon per hour. The cost of propane is running around $2.25 per gallon so the cost to run the generator for 48 hours would be $108. BTW, this should tell you what a bargain utility power is. The good thing about a generator is that you can have backup power as long as you have propane. A propane supplier can help you pick the correct size of tank. At our new house that is almost all electric but with a propane range top, propane fireplace, and outside propane connection for a grill, we will have a 22KW generator and a 500 gallon tank, overkill for your application.
Here is a link to the generator I mentioned:https://www.electricgeneratorsdirect.co ... 02402.html
I hope this is helpful and that I have not overloaded (pun intended) you with info.