I grew sweet potatoes twice. The first year, the vines took over "their" area and way more, so the next year I grew just 3 vines, and they sure spread too.
Since I have a short season, I had to get shorter season varieties, and I don't recall what they were.
Curing... They need a warm, humid spot to cure so that the starches convert to sugar. Warm was supposed to be 80+ degrees and humid was supposed to be 85%+ RH. I don't really have a place like that, so I got inventive. For awhile, I had them spread out on tables in the green house. Since I had to let them grow as long as possible, the green house wasn't warm enough in short order.
Next stop was on the dining room table. I had them in large clear garbage bags, covered with my electric blanket. I monitored the temp with a thermometer to keep it around 80-90 ish.
Some of them got a bit of mold in the bag, but most were ok. I stored them in the basement. We didn't eat that many, and they didn't store that well. Some rotted, some got moldy.
Since the ROI was rather low, I haven't bothered to grow them again.