Since I overwinter my container ones in a greenhouse, I know little about keeping them in a basement, though I know of many who do. I can answer about the cuttings though, should you decide to cut them back to make for easier storage. I simply put mine in water (six inches or so) and allow them to root over the winter. Brugs can take temps down to the freezing mark with no damage, but will freeze below that. Hopefully, someone else in your zone will chime in to give you explicit instructions for overwintering there. Good luck.

I move mine to a cool, darkish basement to go dormant. They get a sip of water every month or so. I try to leave any trimming to the Spring, so if there's any die-back I'm better able to judge a balanced shape for the next season.

I'm in zone 5, yes i do have a greenhouse but this is what I have noticed in the 5 or 6 years that I have grown them. by Oct. 15th i dig them up out of the ground ( they grow much better and bigger in the ground! ). I cut all the branches off so all that's left is the trunk maybe 2' tall. Knock off about half the dirtball then put it in a tub to hold the plant with some soil. The trunk will always back-bud, so by spring ( May 15th ) they will get planted back into the ground. Yes my greenhouse is barely heated, just so it doesn't drop below 38 degrees. I don't know how well storing them in a dark basement is but they love to grow. My burgs trunks are all about 3-5" across. I just cut my salmon colored burgs down, my yellow one blooms a little later. It's peaking in buds right now. All the burgs will get to be about 8-10' tall with a width of 6+ '. Want more cuttings in the spring for summer blooms, take loppers to any brnch and then shove it into the ground and keep moist for afew weeks then let it grow.

My potted Brugmansia have their leaves stripped off and are transported to a dark corner of the basement for overwintering (watering every few weeks to assure survival without promoting new growth - any that occurs is promptly removed). I have tried keeping plants in growth with artificial light, but the plants are so prone to whiteflies and other bugs that it's too much of a pain to keep them sprayed and (relatively) bug-free.

The ideal would be a cool sunporch that stays in the 45-60 degree range, but few people have one.