Publishing in early career
If the research is good enough, it will get published. The challenge is to do good-enough research as a sixth-form student. Actually, that's a challenge for any of us, at whatever stage we're at. The best example I know of, of young researchers getting published, is a paper in Biology Letters from a class of 8-10 year olds. The paper, Blackawton Bees, is a good bit of research and an entertaining read.
Principal finding ‘We discovered that bumble-bees can use a combination of colour and spatial relationships in deciding which colour of flower to forage from. We also discovered that science is cool and fun because you get to do stuff that no one has ever done before.
Actually, never mind the rest of this answer for now. If you're reading this, whoever you are, and you haven't read the paper before, just go read it now - it's free to view for all. You'll thank me (so remember to come back here afterwards ;-).
Journals for students
As far as journals specifically for students: well, they all are, really. Pretty much all of us who are reading them, are reading them for study. God knows, they're almost always so dryly written that no one would read them for pleasure.
There are exceptions. For easier reading, there's New Scientist and Scientific American; though the science sometimes suffers in the cause of circulation-friendly journalism, particularly for New Scientist.
More digestible science
And there are quite a lot of science blogs on the web, which make for more digestible reading of recent research. Unfortunately, there's also a much higher number of pseudo-science blogs on the web, that, unless you know a lot about the subject, are hard to distinguish from real science, but contain pure unadulterated nonsense. For example, Real Climate is respectable science by respected scientists; Watts Up With That is unadulterated pseudo-science nonsense; but to the unwary, they are both climate science blogs. So, for finding new science blogs, reader beware. Even well-established science blogs sometimes go off the rails, when they stray outside their area of immediate expertise.