You need to go to the allopathic forum. Theres a lot of debate on this actually. (scrubs, not lab coats)
In med school you will get a short lab coat. Once you graduate, you'll get a long one.
As to wearing scrubs, you will follow whatever your institutions (or dr's office) rules are on wearing scrubs. Generally if on call, it is acceptable to wear scrubs, but not if you are in clinic or working a regular 10-12 hour day. As I said previously, this will change based on what everyone else does at the hospital or office you work at. A lot of places will expect physicians to look "professional" which means dressing up. I personally think scrubs are great, but apparently not everyone agrees. Like I said, look at various threads in the allopathic forum, quite a few individuals think scrubs are sloppy and unprofessional and don't belong outside of being on call or anatomy lab.