That's a healthy budget. Since this is your first knife, I'd recommend something moderate in the $100-$200 range to get you started. Most people eventually end up buying more than one nicer knife, and it really helps to know what you like and what to look for when you make your next purchase so save your money on the first one. Since you will be sharing this knife with your girlfriend, I'd recommend a 210mm gyuto, or 8" chefs knife. If she's like most women she'll be intimidated by anything larger than that. Since you didn't mention a preference for carbon steel or stainless steel, I'll assume stainless steel would be the better choice since it requires less care. A "gyuto" is commonly available with a Japanese style "wa" handle or a western handle, and again I'll assume western handle in this case.
I haven't heard a lot of buzz about this knife recently, but it's gotten rave reviews before - Sakai Takayuki Grand Chef in 210mm with western handle. The steel is AEB-L and is the same as what you'd find in the DT ITK mid tech knives for hundreds more. I'm sure the heat treating is different, but the steel is the same. Excellent edge retention and great geometry in a stainless knife that doesn't break the bank.
There is a wealth of information available here, so if you care to look further you can educate yourself on steel (carbon vs satinless) handles, knife types, makers, and just about everything else you can think of regarding cutting things in the kitchen. I'd also recommend giving some thought to sharpening your knife. Learning to sharpen will save you a great deal of money in the long run and can be a rewarding experience. If you don't want to that's ok too, but keep in mind that the knife will not stay sharp forever. You'll eventually need to send it out for sharpening or take it somewhere to have it sharpened. This can be expensive. Be wary of anyone who seems to charge much less than reputable sharpening services, lots of people out there have no idea what they're doing and can ruin your knives. You could also try a half and half solution of sending your knives out, and touching them up yourself regularly on a strop or honing steel. This will extend the edge somewhat, but the knives will still need to see stones at some point.