What size kettle should I buy for various batch sizes?

5 gal batches: 10 gal kettle

10 gal batches: 15-20 gal kettle (depends on preference / a few variables)

1/2 BBL batches: 30 gal kettle

The general rule of thumb is you would want to be just under double your total finished batch size in your boil kettle just to give you some room and /or mitigate boil overs, etc.

There are many spirited discussions around what "exactly" should be  - but as usual everybody is right!   Above is just our opinion/guidance.  And on the 15 gal kettle - some would say enough for 10 gals and some would say not.  You are both right!