Every effort needs to be made to contact the site's authors to see if it possible to take it over. I have tried this on two separate occasions and both times I was asked for money. Both times I refused to pay. One site remains available but has not updated material in months, while the other has simply ceased to exist.
Reproducing information without permission is always dangerous. Original material has a copyright attached to it, which lasts for many years after the death of the author.
More importantly, as we have seen with technology such as GIFs, the intentions of the originator do not determine the conduct of the heirs. In other words, someone could come along and declare the material is theirs and they want to be compensated for its use. This is a problem whether or not you derive income in any form from your website. It may be possible to approach the problem the same way as Google. They often maintain a local copy of pages they index. The pages, however, are only accessible through a search engine and are not otherwise presented as a structureed product.
The key to this is the site's robot exclusion policy. A trick of journalists and academics is creating new work based in part on the prior work of others. Copyright allows material to be quoted in this manner. You just need to make sure the new work is substantially your own. Your work could be a review or a critique of the original with substantial quotes included to help make your point.

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