Old house, no ground wire, hoping for protection of new computer?
You are correct about GFCIs or ground fault devices.  In an ungrounded situation, GFCIs are a cure-all for life safety, but they do absolutely nothing to reduce ESD damage to equipment.  For that you need proper grounds.  

Normally, when a technical person says they are reluctant to mess about with mains power, I encourage them to listen to that voice.  However, in 2014, they broadly legalized retrofitting grounds.  And retrofitting grounds is a job that matches well with knowledge that is "technical, but not electrical", or that is "electrical, the wrong kind".  

Retrofitting grounds is, in a nutshell, you run a ground-wire backbone between all your heavy appliances (A/C, range, water heater, dryer) and the braided copper grounding elecrodes leaving your panel.  This is done in 10 AWG wire.  

Then, off that, you branch outward to all the other outlets.  Any outlet needs to either reach the backbone, or another outlet that reaches the backbone and has large enough ground wire all the way back.  Best to use #12 wire for this. 

If the boxes are metal it is sufficient to clip it onto the edge of the box.  Otherwise adding the grounds is no more difficult than changing a receptacle or switch. 

You put the ground wires wherever practical, it's not important to follow the same route as the conductors.  (You won't get EMF loops and eddy current heating because grounds don't carry current except during fault conditions.  

Now, lastly, the old conductors.  Another device is a cure-all for ratty old conductors also: the AFCI or arc-fault breaker.  It looks (literally, it listens) for loose connections, inter-wire shorts, or other arcing - it's that scratchy "hooking up speakers with the amp turned on" or "jiggle your headphones in the jack" sound.  They are about $40 a pop, or you can get a combo AFCI/GFCI breaker for about $50.  Unlike GFCI, AFCI needs to be at the breaker because it protects the wiring, not the outlet.