Usually I prefer to go just 1 size down ... meaning in your case, 17" would be ideal.
Used rims & used tires can be found in Kijiji and here http://www.e90post.com/forums/forumdisplay.php?f=300
Winter tire size (proper fitting) would be 225/50/17 H or V speed rated, if possible as to maintain the stock spec.
Within the winter tire grouping, there are the winter performance tire and there are the snow & ice tire. Both group of winters have their advantage & disadvantage. In general, given the T.O. past couple of winters, I feel you should be alright by choosing the winter performance tire as they handle better in dry cold winter weather.
Since you are trying to buy used, then if you are able to find a set that are mentioned in that link, along with priced reasonably, then you should consider it.