A vine. Wondering how you came by it. Was it being used as a vine and how will you get it into a pot.
Cuttings, yes, can be started either softwood in the spring's first blush, or take some pieces now and give it light that is not direct. East and north-east window would be ideal for its light requirements now but as winter approaches and the sun's intensity goes down it would be able to put into the window more.

Catharanthus has all its parts though toxic...so would be better if you don't have a pet...a cat or dog that would ingest it.

Vinca minor, maybe? I've seen a white-edged green vining Vinca like what you're describing; we sell it at work. (I don't know a variety name, but maybe the species will be enough for Google to turn up a picture?)

It overwintered fine in the greenhouse for us last winter. We cut the stems back to about three inches in September or October and put it in a cool (50s-ish) bright spot under a table. We never watered on purpose, but it did get water, from what dripped down from the table. Roughly 95% of the plants made it.

I don't know how practical this will be for you if you don't have a greenhouse, but maybe a bright spot in a porch or garage could work?

It's probably Vinca minor 'Variegata', a true Vinca and not Catharanthus as was suggested earlier. It's commonly sold as an addition to container plant groupings, or as a hanging basket by itself. I'd give it as much light as you can find in the house. Outside, it prefers a bit of light shade. Finding that cool location would sure be a plus, too.

Attached is a photograph of this plant, just to see if it matches yours.

Here is a link that might be useful: {{gwi:99133}}

Vinca (I think it's V. minor) has naturalized itself here and I see it growing green up tree trunks in the winter. I imagine it's pretty hardy and would be something I'd pop into my garage for overwintering, where the temps get perhaps low as 50F. It's pretty tough stuff.
-perL

Do I cut back the vinca's or leave them in the pot long as they are winterized in the basement?

I came across this old post by chance. Violet Stevenson, an old houseplant writer, said that Vinca minor was grown in Scotland as a houseplant very successfully, and that her grandmother had one. However, it was Vinca minor, the one with the small leaves, I don't think the one in the picture above is V. minor. There are a lot of beautiful varieties of this plant, there are ones with silver variegated leaves, golden variegation, white flowers, blue flowers, purple ones, and single, semi-double and double flowers. I plan to give them a try indoor next winter. I will shortly post a picture of some different varieties.