I have two degrees, one in information systems and one in law, but I did not need either in order to secure the work that I have. They have helped in cases of negotiation, but the degrees themselves are not why I received referrals. I received referrals because I was able to prove my skills to prospective clients.
I learned how to develop web / desktop applications from a rather early age, and these days it is much easier to learn very quickly how to do either kind of development. The first degree taught me more about project management and adhering to large corporate procedures, but they are not necessary if you are taking on smaller business style projects.
I do suggest you start that route I mentioned, as it is a quick way to both find and retain clients, as the work at that stage is minimal. If you have more to offer, that is great, but gaining your clients' trust and confidence is most important. They will then be willing to pay higher premiums on further work you do for them, if you decide to do that. How reliable you are perceived to be will greatly affect the kinds of offers you will receive. You could otherwise simply do these basic tasks as a consultant and become an expert at those basic tasks, ensuring you a very steady stream of income, but that is up to you.
As a business model, if a large proportion of your contracts are for basic tasks, you will earn enough to maintain yourself and invest in any tools (computers, software, server hosting) you might need in order to carry out a few contracts with some complex tasks, which will provide you the higher premiums. I would not focus strictly on complex contracts as it could be risky.
Where you end up taking your portfolio will really depend on the what kind of work you find available, so to get the more challenging opportunities, starting off with the basic tasks certainly helps.
EDIT: Search engines will be your best friend as a freelancer, as you will be able to take the time to read the necessary documents and tutorials prior to learning how to do the various things a freelancer will execute on the job.