Need help buying the right sized off-grid solar system
There's no magic here. Plenty of engineering, though.
Yes, the inverter output needs to be greater than your peak load.
Not only that, your battery bank size needs to be adequate that the peak load is not exceeding the battery bank charge drawdown rate. Hint, yours is not - you're contemplating drawing over 100 amps at 24 volts off a 200AH battery, or C/2 - that needs to be about 10 times bigger for the usual C/20 that solar storage batteries are designed to tolerate.
That's harder with cheap but fussy lead acid batteries and easier with expensive but tolerant (except where they are not) lithium batteries. In both cases reducing your peak load is usually the most cost-effective option before any others.
Off-grid solar is expensive. In many locations, the &quot;average full sun-hours per day&quot; is a lovely figure that is essentially useless for the month you have to design for (in my area, November - gray and terrible from a solar point of view. If you can make it through November here, other months are easy, but enough solar input and batteries for a non-grid-tied November is daunting/expensive.) That also means that you have excess power (and no grid connection to sell it) most other months.
Those cheap but fussy lead acid batteries have limited lifetime and limited tolerance for being deeply discharged, which is one thing that makes the ongoing &quot;cost per kilowatt hour&quot; significantly higher than grid electricity, in most cases. The popularity of grid tie is in part because it's like having a really, really good battery 99+% of the time, and the maintenance is just paying for your connection fee, which is usually a lot less than paying for a few tons of batteries every few years (perhaps longer if you are very careful with them.)
I spent a while designing a solar system for my place, since the power company and neighbors were being uncooperative (the power line is not quite on the road, so an easment to get it to the road and then to my place was needed.) It was a heck of a lot of money. Fortunately the neighbor situation changed, and then the power company became cooperative, and it was still a heck of a lot of money to get the grid, but it was a lot less money than off-grid would have been, and lacked some of the limitations (I was going to have to have a generator to run for heavy loads that could not be reduced.)