There may be a short-term benefit if you list "Reviews for X" on the CV, or the journal publishes a thanking-by-name for the year's reviewers. Otherwise, the outside world would have no idea whether you are a diligent reviewer or otherwise. Another medium-term consequence of diligently reviewing, especially if your reviews are high quality, is that editors may get to know that you are a good reviewer. This can lead to invitations to serve on editorial boards and perhaps the ultimate horror, being invited to take on an editing position. IMO, if your concern is getting a permanent job, the value for that goal of reviewing is pretty low: it's more useful for tenure and promotion, especially promotion to full when service counts more.
Taking a more long-range perspective, reviewing is in your self-interest for two reasons. First, you can influence the shape of your field by imparting your knowledge to other authors via the reviewing process (thus making the world more friendly to your viewpoint). Second, if you encourage and support the existing system of volunteer scholarly reviewers by reviewing, then (by "cultural osmosis") your own submissions stand a greater chance of being reviewed appropriately. That is, if almost everybody says "No way" to review requests, then there will only be a few reviewers and the reviewing system will collapse, which would not be good for your own publishing plans.
But of course, avoid junk journals and don't automatically accept all such invitations, not at this stage of your career.