It seems fairly clear (at least by the end of the story) that the demon's target is Karras. The following exchange comes as close as anything to stating this explicitly (from IMDB quotes):
Demon: What an excellent day for an exorcism.
Father Damien Karras: You would like that?
Father Damien Karras: But wouldn't that drive you out of Regan?
Demon: It would bring us together.
Father Damien Karras: You and Regan?
Demon: You and us.
Remember that at the time the demon seemed to be trying to deceive Karras by referring to itself as "us" (perhaps because Karras is a psychologist. He talks about having identified at least three personalities inside Reagan, it's a sort of thing an author might imagine that a psychologist would do :).
At the very end of the story, Karras explicitly invites the demon into him and it immediately does so. This suggests either that Karras was its target all along or that it wanted or required a willing or otherwise suitable host.
But this doesn't answer the question of "Why Reagan?" There are two major possibilities, neither of which is contradicted, as far as I remember, by either the book or the film.
The first suggestion is that the demon is an opportunist. It finds a way into the world via Reagan, perhaps because of the Ouija board, perhaps because she's lonely and a little neglected and therefore more susceptible. She has no understanding of the concept of demon possession and is apparently not freaked out by the fact that an invisible presence is talking to her. This suggests isolation from her peer group, as does her itinerant and protected lifestyle. The implication seems to be that the Ouija board got the demon's attention (otherwise why mention the board at all?) and that her isolation helped the demon to take hold of her. Reagan was also a good choice because her mother was oddly ignorant of the concept of possession too. Also, being an atheist, she made the reasonable assumption that Reagan's symptoms were caused by medical or psychological means. It's also worth noting that Reagan's mother was rich and powerful, which might be a useful tool for a demon intent on mayhem.
If the demon was simply taking an opportunity, then it would have found Reagan a good place to start. However, if Reagan were its ultimate goal, why didn't it just quietly inhabit her until it had opportunity to cause whatever mayhem it wanted? Why all the theatrics without actually achieving anything? Perhaps, as I said, it needed a willing host. The theatrics eventually caused Reagan's mother to believe in the possession. Perhaps it was looking for a particular kind of host: a priest? Someone with influence? Something more specific?
However, if Reagan was an almost ideal initial target for the demon, Karras was a good match too. He was losing or had lost his faith. He was a psychologist, so would be drawn to Reagan's case. He was grieving and feeling guilty over his mother's death. It seems likely enough that the demon would wish to infiltrate and corrupt the church and possessing Karras – someone who worked with other priests having crises of faith – would be an excellent way to achieve this.
All of this could have been orchestrated by an opportunistic demon and a favourable set of circumstances. However, the second suggestion is that Karras was the demon's intended victim after all. There's some circumstantial evidence to suggest this, but if so it was a very convoluted plan with many points at which it could fail (which it eventually does, of course). The demon seems too cunning to rely on such a complicated set of events.
Nevertheless, there are some indications that it might be the case. For example, Reagan's first instance of really odd behaviour was the party scene, which happened to be attended by a priest; Father Karras' friend. Reagan's mother had already noticed and been impressed with Karras, especially by his intensity. She asks the priest about Karras and this conversation is part of the reason she eventually contacts Karras.
Reagan's doctor (and later team of doctors) believe at first that Reagan's symptoms are medical. When they have exhausted that possibility, psychological means are sought instead. When that proves fruitless too, the exorcism as a psychological tool possibility is raised. The demon was in a position to manipulate Reagan's symptoms to this end, but why bother? I think this is the strongest evidence that the demon might have been targeting Karras all along, presumably because of his wavering faith and his position in the church, which would have made corrupting other priests very easy.
I favour the interpretation that the demon was an opportunist and a skilled tactical manipulator rather than a master strategist. It's the simplest and least convoluted explanation. But as far as I can remember, neither explanation is contradicted by either the book or the movie.
So to summarise: "Why Reagan?"
- If the demon was an opportunist, she was an easy target.
- If the demon was after Karras all along, she was the best means to get to him.
There are some suggestions in this thread that don't seem to be supported by either the movie or the book.
That the demon entered Reagan because she had started masturbating. As someone else pointed out, there is no mention of masturbation until the incident with the cross, which occurred after she was possessed. Besides, it doesn't answer the question of why Reagan because everybody masturbates unless it is physically impossible for some reason. Why isn't everyone infested by demons?
That Reagan had previously committed murder. There's no suggestion in the text or movie that this is the case. It seems likely that the demon murdered Dennings via Reagan but again, this is post-possession. The line about "do you know what [your daughter] did?" was delivered in Dennings' voice, after all, and clearly refers to his death.
Sexual abuse. Other than her mother and the nanny, Reagan didn't seem to have contact with... well... anyone, really and there's no suggestion of sexual abuse of any kind in the book or movie. The suggestion that Dennings might be abusing Reagan is not borne out. There are many reasons for Dennings being in Reagan's room. The demon could have made her scream for help. It could have called to Dennings in a voice he recognised. An adult being in a child's room is hardly a conclusive indicator of sexual abuse.
We're all speculating about a work of fiction in any case, of course.