Just ordered more memory, with the blessing of my wife. Woot.
Hopefully the Sims will be faster now, with less disk thrashing and churning.
(Upgrading from 512 MB to 1.5 GB.)
The model computer I have (which I couldn't accurately determine, but may be "MD 8088" or "PC MT 6") wasn't on their website under "Medion", but I picked "MD 8080", which seems to match what Medion says about memory expansion (viz., 4096 MB total memory, PC 3200 DDR). So hopefully what I ordered (1 GB kit/512MB x 2, 184-pinn DIMM "Upgrade for a Medion MD8080 System") will fit. Two modules because apparently the memory must be installed in pairs.