Don't like that much big single cylinder like this.
Too big for one cylinder. After 15HP it's better to have a Twin (but not the same price, and can be complicated to re-power your mower).
31 series B&S will work fine and be a direct replacement except may have to check alternator which will interchange if necessary. Be a lot easier found if you are looking for a used one.
Any engine with the same output shaft diameter and length will fit.
Using the same brand & series just makes it easier as it is pull out drop in plug up & you are good to go.
Check out the surplus engine suppliers and the surplus centre for available engines at big discounts.
If you go with another Briggs the only thing to watch is the alternator output.
However all Briggs alternators interchange so you might need to swap the stator And perhaps the flywheel ( cant swap between single & twin flywheels ).
A twin will be better than a single just check the dimensions so it will fit.
Other things like exhausts are a bit more difficult as they are part of the mower & not the engine.
Lots of engines at this time of year
I like to buy "pulls" because they are scratched from being fitted so go for a lot less.
A strait engine swap is about a 2 to 3 hour job.
Just make sure you thread the mounting bolt holes before you place the engine otherwise you will need some one to hold the engine and push down on it while you try to force the self tappers in from underneath.
The direct replacement is model 33M777-3036-G5 which is plug and play, you will need to use your muffler. It should be less than 6 bills. You could also short block but that will be more expensive than a complete engine.