Where do I begin finding estimates for problems with my potential first home?
Take a walk through with the home inspector and see what he says.  If you are still interested in the house, find a good general contractor (that you trust) and take him on a walk through.  The contractor should be able to give you a good estimate on what it will cost to fix any issues, he may also give you some price breaks if you are willing to let him handle all the work.

Just make sure you are comfortable with the contractor before you ask them to go on the walk through, they might be upset if they take time to walk through with you and then you find a new contractor to do the work.  Keep in mind, however, that if the contractor starts work and does a sub-par job, you can always fire him and find a new contractor.