I can see current challenges (a specific number of kills for a specific weapon) and their bonuses when I access the challenges screen but I'd like to find a comprehensive list. Does this list exist yet?
In general, there are XP rewards for a certain number of kills with each weapon and there are attachment rewards for a certain number of kills. Attachment rewards are only for primary weapons. Listed below (from this page) are the XP rewards and the attachment reward levels: