I do have a countertop still and it's nice when I want to futz around with a new idea or make small batch stuff. I enjoy gin for instance, but rarely want to make several gallons at a time.
Why fire up the keg still and worry about if I have enough propane or a whole day to devote to it, then end up with several cases of stuff I only drink occasionally. Rum or whiskey, sure, fill the keg with low wines and I'll drink it eventually. But absinthe and gin get the countertop treatment for making two or three bottles instead.
I was unbelievably lucky to find my 2 gallon water distiller at a thrift store for $5 (it's a $750 machine) so I can't recommend a particular vessel, but the common coffee pot still design I am aware of uses a borosillicate glass coffee pot so it can be put directly onto your kitchen stove, gas or electric.