I know a little bit about consulting and development and perhaps I could give you some advice.
The most natural thing for you would be to look for a development-related consulting position (I could suggest Dalberg Consulting, a pretty good firm in this area). However, to work in development stuff in the long-term you're better off acquiring a basic set of "corporate/for profit" skills as they are extremely important for NGO/International organization work. In fact, most organizations, such as the World Bank, would always favor people who have some decent experience in the corporate world over people who only have experience in the development arena (trust me, I know about this). Therefore you should try to put a strong brand name on your CV. Note that the brand name is perhaps more important than the actual work you do. It matters that you get a decent set of business skills, but how you get them or where you get them is not that important.
You should take into account that views about different firms change in different countries. And, even though I know that people will find it hard to believe, the brand value of firms like Deloitte, PWC, KPMG, E&Y or even Accenture in developing countries is far greater than the value of other stronger consulting firms (ie. MBBB), which are better recognised in Western countries. This is due to the fact that Big4 firms operate in countries such as Malawi, where none of the MBBBs does much work in there.
This will also help you because it will be easier to get into a Big4 firm for you than to get into a MBBB.
With regards to your background, I would argue that it could be an advantage for you. Let's face it, graduates rarely have any useful skills to bring to the table and they often get on-the-job-training to get them going. Consulting firms (especially if your 1st class degree is from a reputable university) would like your unusual background and if you know how to sell yourself you can easily get an analyst position at a good graduate scheme!
All the best,