Well, being in a sharing mood, I'll give you some personal details as to picking a specialization. The first step for me was discovering an interesting thing about languages, namely that English, Norwegian, Latin, Green and Sanskrit are historically related. I studied up on this matter and by the time I was in college I was committed to the idea of studying this ancient reconstructed language, Indo-European. I did this, but of course you can't just take classes in Indo-European (there was exactly one such class in the day, and they don't teach it anymore), so I took regular linguistic classes. Turns out that syntax and phonology were very interesting to me as well, so although I finished an undergraduate program with a thesis on Indo-European, I had mentally switched to "grammar" after the first two years.
The switch involved a number of aspects. One was my realization (thanks to an eminent professor who later became a colleague) that I really lacked the requisite background for doing Indo-European linguistics (requires fluency in Latin and Greek by high school, etc), and a second was a fundamental disagreement with the methodology of Advanced Indo-European linguistics (not basic comparative linguistics).
I had excellent teachers in syntax and phonology, so there was no essential flaw in either area that repelled me, but at least at the time, syntax was entirely about English, and phonology was (becoming) about other languages. I got into linguistics via the path of acquiring languages, so there was a natural attraction towards phonology. One of the basic problems I did have with syntax is the data problem, and the epiphany came for me when we were doing "Remarks on Nominalization", where Chomsky gives a perfectly grammatical example of tough-movement out of a nominalized clause, and it was essential to his analysis that this be ungrammatical. Apparently I was not the only person who rejected his data claims, because he makes the bizarre claim that speakers who accept his starred sentences are "not aware of an internalized property of their grammars". Whereas: once you toss out some of the silliness of Sound pattern of English, phonology was based on decent data claims.
Then finally, at the crucial moment, one of my phonology teachers wasted hours teaching me practical epistemology. So that's how I got here. In other words, I was in search of an intellectually interesting domain that could be a career, and I found it.
