Most journals don't like people "scraping" papers, even if it's only a small-scale effort. Tread very carefully. Aaron Swartz was prosecuted (admittedly he did download over 4 million papers), and later committed suicide. Although a small-scale effort is perhaps unlikely to attract much scrutiny, it's still probably against the ToS, which is why no one has published software to automatically download papers. An exception is the arXiv, where you can indeed download everything, if you pay them for the bandwidth.
There are tools to help generate "networks" of papers - Web of Science, Paperscape (for arXiv papers), and ADS Labs (in case you're an astronomer) are some examples. There might be more field-specific repositories that have similar capabilities. But typically these tools will not just automatically download a whole folder full of PDFs for you.
In my experience (and especially if you're dealing with older, scanned articles), searching by keywords and citation maps only will lead you to miss some useful papers. You do need to actually put in some effort yourself in the search! A sound approach is to start by reading a few key literature reviews in the field. Read the useful-sounding papers those authors cite, as well as all of the highly-cited papers in the network. Rinse and repeat.