I honestly don't know much about buying a house, but here are some things I thought made sense:
1. Compile a list of things that you must accommodate for, such as disabilities, future children you want to have, travel (public transit nearby, or a highway, etc.) At the same time, compile a list of deal breakers (previous owner had a deadly contagious disease, etc.).
2. Going off the previous one because it is so important, transit. Make sure you aren't out in the boondocks without a car. Is there a garage?
3. Is it safe? Some houses pass inspection but can be dangerous. Narrow hallways can be dangerous in cases of fire (doorways can also easily block narrow hallways). Will it flood when it rains and/or snows?
4. Consider the neighborhood/neighbors. Be aware of any potential problems such as loud mean bulldogs next door.
5. Maintenance. Will you be able to take care of a front and back lawn? A pool?
6. Obviously be careful with finances. Have an agreement to settle things financially if not everything works out long term with the girlfriend (Hope you don't have to, but it's just a good idea).
7. Ask the real estate agent about the history of the house. I wouldn't want to live in an old crack house. Watch for things like asbestos and mold (obviously).
8. Make sure you really like it. It needs to fit both you and your girlfriend's needs. Don't buy impulsively.
9. Insurance - Not everyone has it for their house, but you may want to think about it and any potential hazards in the area like weather.
Good luck! :)