What's the accepted "abbreviation" for the original iPhone?
Unlike the newer iPhone models, the first iPhone did not include UMTS/HSDPA - also referred to as 3G - but only GSM/GPRS/EDGE, which are referred to as 2G.

The terms 2G, 3G and 4G refer to the x'th generation of a cellular wireless standard. 

Therefore, you can search for cases that refer to the iPhone 2G. If you want to be abosultely sure, use the model identifier number when searching: A1203.

Terms used for the first iPhone include:


original iPhone
iPhone 2G
iPhone EDGE
iPhone 1


Here's an overview of celluar standards from Wikipedia: