Moved into house with only 2 prong outlets. What to do with fridge and other outlets?
According to the article at this link, replacing an ungrounded receptacle with an ungrounded GFCI receptacle will offer more safety than an ungrounded receptacle (with presumably a 2-3 prong adapter). A fault in the plugged-in appliance will still trip the GFCI even though there is no path to ground. This seems highly superior to using a 2-3 prong converter with a do-it-yourself ground path, as that would just allow any stray current to follow the ground path versus tripping a GFCI. 

http://communities.leviton.com/thread/1080

I don't know why a fridge would trip a GFCI.

Assessing your risk is a bit tougher. In my simple mind, user-triggered electrical faults come in two basic varieties - overloading the circuit or providing an alternate current path to ground. Do you plan to run extension cords under carpets? Are your electrical items in good condition - e.g. relatively new, no frayed cords, etc? Do you plan to use any appliances in wet conditions? GFCIs protect against these types of faults. If you are careful in these areas, there is less risk. Most home receptacles don't have GFCIs unless they are in damp locations (e.g. bathrooms, kitchen, outside). So I would focus on these areas first. 

Here is a great article on why some appliances have 2- versus 3- prong plugs. Maybe it will help you assess your individual appliances and usage for risk.

https://www.quora.com/Does-the-third-ground-prong-on-electrical-plugs-improve-safety

GFCIs do not protect against circuit overloads. (Overloads may happen either from plugging too many things into the same circuit or from a short circuit.) That is what fuses and circuit breakers are for. They work regardless of the presence of a ground wire. As an owner of a couple of rental homes, I am as concerned about overloading the circuits through normal use (resulting in wires overheating in the walls) as I am about electrical faults (which may do the same thing, but it requires a failure versus a situation that may occur during normal day-to-day activities). If you have a lot of equipment that draws power (kitchen appliances, space heaters, amplifiers, etc.) you may want to figure out which receptacles are on separate circuits so you can spread out the electrical load. The fuses/breakers should protect you against overload, assuming the system was built/updated to code. But if you don't want to assume, you might want to think about how best to plug in all the stuff you have to distribute the load as evenly as possible.