Where to publish your work
There are different journals that publish law and economics research. They differ in the methodology they accept, style and prestige. Bellow you may find some of the most important law and economics journals, and more legal journals. This is not an exhaustive list. The choice of a journal is very important in terms of your future career, therefore, take the time to study the journals and the expectations of your potential future employees.
Main Law & Economics Journals
American Law Reviews
Those are usually student-run journals. Law reviews provide an additional opportunity for publications. They are very well cited and provide your work wide exposure to academic and professional audience. However, law reviews differ in their prestige and impact, therefore, study them before submitting your article (you can see their ranking here).
There are two websites where you can submit simultaneously your article to many different law reviews (check for exclusivity policy). The submission is for payment but many universities have a subscription. Those websites provide detailed instruction of the process:
Where to present your work
Making your work visible to others and receiving feedback from peers is an important element of academic career. Search for different opportunities to present your research. Bellow you find the main law & economics conferences. This list is not exhaustive, and you might want also to search for conferences specific to your field of research.
How to make your work in progress visible
There is also an opportunity to upload your working papers online so people can read it even before you publish. This way you can also follow the work in progress of other scholars in your area (or from other, interesting areas to you). Here are some links: