Currently on ebay there is a Lady Cobra iron set for $80. Callaway Big Bertha and Steelhead driver/woods are $30 each(originally $200-$300 new). Just be sure to buy the same model for driver/wood. But you still need a bag and putter. Perhaps you have a friend or a local First Tee program with an old unused bag?
Good advice from all. Absolutely nothing wrong with getting that Aspire set the other guys are mentioning because it includes everything you need. Actually my wife did start that way; but we ended up spending more money to upgrade; thus my advice as it is. My daughter got her old starter set. If your girlfriend is young and a natural athlete; she will learn fast and her competitive spirit will want to improve. If she is just average; a starter set should be just fine.
In my limited experience; beginners will find their comfort zone in only 3 or 4 clubs. For my wife and daughter it was the driver, 5 wood, 7 and 9 irons.
One last suggestion. Spend $45 for one lesson with a teaching pro. That is enough to get her started on the right track with grip and swing fundamentals before bad habits develop. It also helps remove you from the competitive bossy boyfriend/husband thing.