It likely depends on the journals to which you are looking to submit your papers. Different journals have different copyright options, some allow you to publish a "draft" (i.e., identical to the final paper), as long as your don't post the actual article .pdf, and you provide a link to the published journals. Others might have an embargo period, after which you are free to publish on your website.
SHERPA/RoMEO provides information on copyright policies for various journals:
If you are at an institution, it might be worthwhile to talk with a trusted librarian, as they will sometimes be able to assist you with negotiating copyright contracts with the journal editor, so that you are able to publish copies of the articles on your website. Authors will sometimes use publishing 'hacks', such as copyrighting or even publishing an article themselves before submitting to journals, so that the author owns the copyright instead of the journal.
Open access journals are another option, although some may be predatory or require a fee to publish your articles. For example, Elsevier charges up to $5,000 if you want to avoid an embargo period.
Overall, is this a good idea or should I strive to rephrase content even if not legally bound to do so?
In my experience this is a relatively common practice, just be careful to follow the copyright restrictions negotiated between yourself and the journals. Rephrasing content is not always a good solution, as some fields consider it unethical to publish the same work in multiple forms/venues.
Elsevier Gold Open Access Price List: http://cdn.elsevier.com/promis_misc/j.custom97.pdf