Sorry, I have no experience overwintering annuals. I planted perennials, over the past 10+ years, in containers and they do well. All are well mulched and I use 12-inch diameter to 24-inch diameter plastic containers. Bigger is better. Maybe your basement will work if you put them under and close to a shop light? That is how I grow my plants from seed. Good luck.

I have overwintered petunias. They managed to survive and produced some flowers the next year but they were not as healthy or floriferous as the fresh plants. I had them in my sunroom. They got pretty straggly by spring and I cut them way back. They did resprout. They petered out by mid summer. Maybe I didn't have the touch. I'd suggest giving it a try. I'd suggest taking cuttings of coleus and sweet potato vine. I'm trying sweet potato vine this winter. So far it has rooted and is looking great. Time will tell on that.

I have had my geraniums for over 2 years now by using stem cuttings and growing these babies. They are easy cause I have a shop light with plant light bulbs and they bloom forever. I have never had petunia outside of my cold frame as it is the only winter protection I could provide for 180 plants including my boston ferns, aloe vera, wandering jews, and herbs. Perhaps using an upside down tomato cage with plastic??