What should we look for when buying a fixer-upper house?
Danny, I respect your enthusiasm. I am a certified home inspector and general contractor in Maine. There's some great advice in the answers here, and I won't repeat the obvious. 

I will warn you, however, learn realtor language. "Fixer-upper" means a train wreck about to happen! Get a real good inspector that has building experience. DO NOT take a recommendation from your realtor for an inspector. Find a qualified builder/inspector. I have always felt inspectors that often work for realtors do not have the buyer's best interest in mind as problems found nix sales and rrealtors don't like that. I personally only work for buyers, never for realtors.

With all that said, renovations can add up fast.  Roof $5,000-7,000, electrical or plumbing $85/hour, bathroom $6,000,  kitchen $15,000-20,000, electrical service upgrade $2,500, windows $300 each, structural repairs, mold, insects, water damage, septic/sewer...

Unless you learn what to look for and are able to calculate the costs of repair or renovation before you buy, you are headed for stormy waters. The joy of home ownership will quickly turn into an unbearable nightmare. 

You mentioned you didn't want to spend $30,000 on a house that you already spent that much on. Where in the world are you going to find a livable house for $30,000? If there is really such a thing, I will buy 10 of them tomorrow and rehab them myself and make a mint, even in this housing market.

I apologize for sounding a bit negative here, but rather be bluntly honest with you considering you admitted you have minimal skills and resources.