A general survey which should include a lift out is obviously a must but usually does not pick out anything you wouldn’t have already observed yourself.
A rig survey had saved me a lot of money as the bow chain plate was starting to lift. This was rectified before I bought the boat.
I regret not having an engine check by a Volvo mechanic, at least for a heads up of what may need attending to after one or two more seasons.
I also recommend a separate electrical survey, first to check overall integrity and also to highlight any modifications that cannot be detected by following the circuit diagram, which I find very challenging anyway.
Hope all goes well. Money up front well spent. Helps you also negotiate a good price.