I've made brandy before from apple wine that turned out alright. Whiskey, rum, brandy, etc. is all a similar process at the distillation level. Make the mash, put it in the still. I made the still from a 1-gallon glass sangria bottle and some copper tubing running through a pot with water and snow in it. Used a drilled cork to adapt it. Set it in a pot of boiling water on my wood stove with spacers off the bottom. The double boiling setup helps to reduce how much water can come off at the end before you figure it out. Temperature measurement of the mash is critical, I put a thermocouple through the cork logged in excel using an arduino and it was easy to see when the temperature started to hook up and the alcohol was gone. A bigger pot would have been nice, I did 5 gallons or so of mash at a time this way in multiple batches and then ran that through a 2nd time. Ran the final product through a britta filter and stored in a mason jar with a small chunk of sugar maple charcoal. Stored in the freezer and wouldn't even hint at freezing at 0F. Tasted like rubbing alcohol/vodka with a subtle apple taste.
Never made rum, but I always felt like the point of homemade wine and distilled spirits was to make it from whatever you have laying around. In our case we make wine from what we pick from abandoned apple orchards, choke cherry trees, wild cranberries, wild black berries, strawberries, dandylions, wild blackberries, beets, onions, etc. If we have an exceptionally large amount of wine, we'll distill it down to brandy. Favorite was some blackberry brandy (not the fortified blackberry juice swill sold in stores). Apple makes the most sense for us due to the massive amounts of free apples around here but I haven't made any brandy in awhile due a massive stockpile of wines/brandy we already have and a lack of time to drink it. Mostly just do a few carboys of wine a year anymore.
"Rum" I believe is from sugarcane which unless you've got it local, I'd think you'd want to consider something else for your base. I think it also has to be aged in barrels to be palatable.
The big thing to realize is the first stuff that comes out of the tube is potentially the nasty stuff (methanol and other toxins) and is the reason this is illegal except for making perfume. It's easy for some duhard to make poison and hand it out at a party. It's subtle, but if you are watching what's coming out of the tube closely you'll be able to see the difference. Have three jars for collection the first time so you can collect each to learn what they look like. Everything's clear, but the surface tensions are noticeably different. You can also practice with cheap wine instead of mash till you get the hang of it.
