There is a house up the street. I currently rent and I think I would like to buy that house.
What questions shoud I ask? What information is most important for me?

The first two questions I would ask myself are, "Why would I want to live there? and "Can I afford to pay for the home?"

There is also lots of information on the following sites that I think you might find to be helpful.

Questions to Ask When Buying a House | NAEBA Agents Protect You

http://www.ourfamilyplace.com/homebuyer/questions.html

The following is from the site: HUD - 100 Q&A for Homebuyers

I would suggest definitely checking out the site for other questions and answers.

1. HOW DO I KNOW IF I'M READY TO BUY A HOME?

You can find out by asking yourself some questions:

Do I have a steady source of income (usually a job)? Have I been employed on a regular basis for the last 2-3 years? Is my current income reliable?
Do I have a good record of paying my bills?
Do I have few outstanding long-term debts, like car payments?
Do I have money saved for a down payment?
Do I have the ability to pay a mortgage every month, plus additional costs?

All of the above were great,

And if you believe you are going to buy, get a complete detailed home inspection by a certified inspector. Check closely for mold, for foundation issues, termites and 1000 other things that can be costly over the short term.

Then of course a title search to be sure the property is clear to be sold.
And title insurance when you buy if there turns out to be a problem