My father used to distill grappa (pomace brandy) for a while. It's legal here if it's for personal use, and we still have a 50 liters copper alembic.
The question is: what do you want to produce? Cheap moonshine or something that tastes good?
Anyway, if you're controlling the whole process I would pay attention to the fermentation: do some research and find a strain of yeast with high alcohol tolerance and good or neutral taste, some nitrogen supplement/yeast energizer and whatever else you need. If you do everything correctly you could end up with something around 14-15% abv and little or no presence of bad alcohols. I do not know what's a cooker/distiller thingy, but if it is small (like, less than 5 liters) you will produce so little of the end product that you might find the whole endeavour unrewarding.
Single distillation (taking care to cut off the head and tail) and a bit (some months

) of aging with wood chips or in a barrel could give you something drinkable if you start with corn syrup/sugar, but I think I would try to distill once, infuse herbs/fruits and distill again. On the other hand, I really like fruit brandies (and here they can get quite expensive), so I would try to get peaches or something and start from the beginning.
And be careful: distilling was fun, but everything ended after one day when overpressure built inside the distiller, the cap literally blasted off and my father (luckily it was not me

) got a few liters of boiling liquid on his leg, causing a nasty (and quite widespread) burn and a number of days of cursing when changing the medication