Brian,
I'd suggest before choosing you that you ask an engineer to provide you a sample report so you understand what you're going to get for your money. The report is something you could potentially use to sue the engineer in future, so there can be a lot of caveats, particularly with a single site visit report. The report will be a structural report of the entire building. If you specifically want damp issues for example addressed, then tell them that up front as it might add to their work.
And, I'd recommend meeting them at the house when they've done a walk through - they might informally give advice that they won't write in report.