To shortcut the process of loading a .pdf into your browser then saving the file from the Acrobat browser plug-in (an extension of the browser (Internet Explorer/Firefox/Chrome...) to allow the display of .pdf files) page, try the following:
Hover your mouse over the document link. If you see in the status bar at the bottom of your browser something like "http:/abc.def.com/xyz/doc.pdf" then the document can downloaded directly by right-clicking on the document and selecting "Save Target As". A file save dialogue box will come up allowing you to specify where and under what name to save the document.
If you get something like "http:/abc.def.com/xyz/doc.htm" or ".html"/".asp"/".aspx" then you will have to follow the link. Within that link you might find find further links that have a ".pdf" form and you can do the "Save Target As" thing.
The advantage of the "Save Target As" method is that you can have multiple (typically 2 to 4 depending upon your browser settings) downloading at once. You may not get a faster overall download time (depending upon your connection speed and how busy the remote server is) but you can set up a few and go get a coffee or do other things.
I suspect on older machines it will have significantly less of a load on the machine as the file will not be loading into the Acrobat browser plug-in but going straight to disk as is.
It also has the advantage that if there is a problem with the Acrobat browser plug-in, you may not be able to load .pdf files into your browser or save them, this bypasses that process entirely and the files go straight to your disk. They can then be read using the stand-alone Acrobat.
To read a .pdf file you do not need the full Adobe Acrobat, just the free pdf reader. If you can save the files using the above method, but after double clicking on the file, it does not load into Acrobat then there is a problem with your Acrobat (a re-installation might be required).