How to arrange a multi-topic academic homepage
My opinion...Perhaps instead of trying to sort the 'topics' or 'content' on the site, you could instead sort by user with a menu bar on the home page.
Have separate tabs/buttons in the menu linking to separate pages: 1 for "Students"; 1 for "researchers/peers"; and 1 for "prospective employers".
That way, you can put exactly what you want that particular audience to see (even if some content is the same across audiences) on individual pages. You will have 1 site, with 3 distinct sets of content arranged by topic independently of each other. On each of those 3 pages, there can then be a specific menu or something for the content on that specific page, for that audience, arranged by either a topic, date, tags, whatever.
Firstly, this question is not really academia-specific, since it is applicable to any relatively complex multi-topic multi-user-type website (or any other information resource, for that matter) - however, I will answer it, since some time ago I was facing the same problem, so I understand your situation.
Secondly, this problem lies within the scope of the very large interdisciplinary field of information architecture (IA) (for some introduction, beyond the corresponding Wikipedia article, see, for example, this page and this page.
Thirdly, there is a multitude of approaches to solving this problem and finding the one ("good way", as you put it), which is close to the optimal approach, requires consideration and prioritization of multiple factors, including perspectives for different types of potential users of the site.
Since different types of users have different priorities and preferences, your analysis will most likely generate several (relatively) optimal designs. As some have already mentioned in other answers, those user-type-based optimal designs might be combined on a single site via tabbed interface, with each tab, focused on a particular type of user. Then, within each tab area, relevant topics can be arranged, based on topics hierarchy, using various methods (smaller tabs, navigational side tree or menu, etc.), plus, the hierarchy's content might be adjusted, based on the relevant type of users and their interests. This just one of the most straightforward and simple ideas. While the sky is the limit in generating site designs, I suggest applying KISS principle to the site's IA for the optimal UX.
There are many nice academic websites out there, but I can't really recommend much due to their diversity and lack of time (I'd have to dig through my vast number of bookmarks). If you care, feel free to visit my own personal professional website, which targets both academia and industry, but academic content is quite limited so far. Please keep in mind that I haven't had a chance to fully update the site in terms of both design and, especially, content, which I hope to get my hands on eventually. Nevertheless, overall IA of the site might give you some useful ideas for implementing on your site (i.e., main menu structure, project types dynamic filtering in the Portfolio section, etc.).
P.S. Despite warning, I have decided to made a quick review of my bookmarks in regard to the topic and here is a tiny subset of academic websites that I find useful, interesting and attractive:
Website of Prof. Donald Knuth
Website of Prof. David Ketcheson (this site uses dynamic filtering approach, similarly to my site's Portfolio section, but it is implemented more comprehensively and in several sections)
Website of Prof. Lorrie Cranor
Website of postdoctoral researcher Davide Chicco
Website of Prof. Aaron Clauset
Website of Prof. Kieran Healy
Website of Prof. Ariel Procaccia
Website of Prof. Theodore Pavlic
Is a typical user a student or fellow researcher? Than focus on them, and keep your material in a way that makes it easily accessible, e.g. by topic.
Potential employers will not necessarily expect to find a resume style first page when visiting your website, but make sure that you make it clear where such a place for them would be. A menu link saying something like "For potential employers", "CV", "About me", are all valid ways. In here, I would have a manually curated resume that puts it in an order that makes sense for the employer.
This allows you to also post informal things, such as blog posts or non-peer reviewed articles that you still think will help your fellow researchers, while keeping your list for potential employers more formal.