BA is Bachelor of Arts, I think the BSc is what I usually see as BSN which is a Bachelor of Science in Nursing. The BN is probably Bachelor of Nursing (either the BA or the BS). The "Bachelor" part means it is a four year program (that some people take longer or do if in less time is irrelevant). BA are lighter on the hard science (like chemistry, biology, and physics) and maybe math requirements and heavier on the language and soft sciences (history, humanities, sociology, psychology, things like that). BS is heavier on the hard sciences and lighter on the soft science.
Either degree could be better for you depending on what you want to do as a nurse. You will get both hard sciences and soft sciences either way, enough to be competent as a nurse but if you want to go into admistration or public health the BA may be better. If you are thinking of nurse practitioner or nurse anesthetist then probably the BS would be better.
BS is much more common and that might be a factor in getting hired but I don't really know about that.