I have mid 2007 C2D iMac with 4GB of RAM.  I hated it while it was running Yosemite, but El Capitan brought new life to it.  It does everything I need it to, but admittedly it's not much, but probably fine for your mom or for a casual PC user.  For me with the 24" monitor it's a perfect media server/client, i file my taxes every year on it, I can run anything on the web with any of Safari / Chrome / Firefox, Youtube, etc.  I host an iTunes server on the machine for other clients in the house serving up thousands of audio and video files.  Since it has a built in optical drive, I ca burn my music CD's.  The kids love watching Netflix on it.  Machine is backed up via Time Machine on an external Firewire 800 HDD.
El Capitan is a free download from the app store,  I have have had to buy Snow Leopard ( I think) from Apple a few years ago for a nominal upgrade ($20-$40), but after that, every OS upgrade has been free.  Machine runs great on El Capitan.