So far, I haven’t tackled any nikaya in a particularly distinct way from one another.
What works for me is to first read all four nikayas once, cover to cover, like any other book. Doing this, I gain a certain idea of scope and a certain sense of what things are covered in which nikaya. I started with Majjhima and soon realized I’d like to bookmark certain suttas in certain groups, so I did the same with Samyutta (starting from II, like dave) and the rest. After reading them cover to cover, I sometimes re-read all the bookmarked suttas of a nikaya, specially of the Samyutta.
But, in parallel to reading them, I started writing on a blog the doctrine “from the start” and looked for a place where I could share what I’ve been reading. I found that Q&A sites (like stackexchange, quora and the one here) are great for this and decided to only answer questions with quotes from suttas (or as much as possible). Same for the blog posts, which are almost 50% sutta quotes.
While a blog and participating in Q&A sites can benefit others in some way (though I’m quite uncertain in the case of the blog), as far as learning goes, I found four interesting things with that.
First, that questions in Q&A would trigger the “I read that recently somewhere”. A few times digging suttas to answer questions and I found that I was developing some strategies to find suttas – what keywords to look for, pali terms associated with passages, etc – and how to bookmark them. I also started having a sense of where important suttas in specific topics are found.
Second, that formulating answers in the Q&A sites and writing blog posts is an emulation of one of the best strategies for learning and retention: which is teaching (Of course, as bonus, one also gets knowledgeable people pointing out where we might be mistaken in our interpretations). In my case, I don’t have any friends or family who are interested in Buddhism, and I’m not participating in any sangha, so I had to resort to the internet.
Three, that, by answering similar questions and writing about them over and over, I noticed I was developing and retaining some stock explanations for doctrines quoting a set of suttas which I often re-read. And when a new sutta was brought to my attention, or a point was raised, or the same topic would show up again, I could revise and expand the explanations I’ve written in the past, but always driven by the suttas and quotes from them. Then the passages gets easier and easier to memorize. The net result is that as explanations become more robust, so does understanding.
Finally, that by bringing up different discourses in difference places to explain something, a fresh new perspective on the dhamma often appears, showing how things relate to each other in all sorts of different ways. Also, there are many subtle sentences that pass by unnoticed when just reading a sutta but, when putting them next to other suttas (distant in pages, or in different nikayas), they become very meaningful.
In summary, I think finding creative ways of explaining and teaching is a very good approach of studying.
However, it has crossed my mind one could probably cover this material well and include almost all relevant points in about 20% of its length! 
There are one or two prior anthologies but IMO the SN is crying out for more (some kind of “Word of the Buddha” just for the SN). Finally, I’d read the FTEB chapter twice, which IMO served as a nice recap, and a good way to get one thinking about the material. Plugged away in that fashion for a long time, then branched out to the rest of it (without aid of the FTEB). However, the sutra-anga is, I think, doctrinally the most important core of it.
(so am not going to give a link).
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