My GE fridge has a 1/4 in OD line, but the connection on the house is larger, and I'm not sure what exact size it is. What is the standard sized connection for the wall valve water supply line?
In North America, standard main supply lines are 3/4" and branch lines are 3/4" or 1/2". The best way to the connect the fridge supply is to put in a T and a shut-off valve with a 1/4" compression connector. The exact valve you need depends on what your supply line is made of (eg, copper or pex).
Another alternative is to use a Saddle Valve. These often come with fridge hook-up kits. Personally, I hate these things. They are easy to connect, because you just screw it on, and then turn the valve to pierce the the supply line. They're also terrible valves, they can typically be used as a shut-off only a handful of times before they start leaking, and the only fix is to cut out and replace that section of supply line (at which point, you might as well splice in the T and proper valve).
If you do really want to use a saddle valve, you should put in a separate in-line shut-off valve. The fridge gets moved around sometimes (Eg, to clean), there are a bunch of compression connections involved.. basically there is a higher-than-normal chance of something leaking, and a shut-off is just a good idea.
My opinion: for the price of the extra valve, might as well do it properly and skip the saddle valve entirely.