Well for the 15.5 gallon kegs the 15" hinged false bottoms are what we sell the most of. That said you can use any size you want really. the 12" is a great choice if your not going to direct fire, want to stay away from the hinged or just dont really want to spend $90+ bucks on your false bottom. I would stay away from the 10" in the MLT but it works good in the BK.
The advantage to the 15" is you can direct fire and drain at full tilt for your resirc, without worring about a stuck mash.
Good luck with the build!