Your questions are pretty general. A lot would depend on where the resort is...domestic/foreign. Size of the police department conducting the investigation. I'm sure most depts would have the ability to take elimination prints at the scene...we used a simple Porelon ink pad made by Sirchie to do that. It was more dense than a sponge type stamp pad. Of course if no prints were found - no need for elims.
A simple burglary/criminal mischief might not get the techs out in a small dept but since the MC may be in danger there is a better likelihood they would or if not able they may call in a larger dept's techs. You're right about many fingerprints in a resort cabin but certain areas could reveal fresh prints...point of entry, personal items, objects that the MC knows have been moved or touched.
An experienced tech usually has an eye for what objects might render fingerprints but not knowing your story and whether a print is important, you have the option of sloppy police work or stellar evidence gathering by someone, oh let's say, old and retired...like me.
Good luck with your story. I'm sure others will want to chime in with more updated information.
Old Bill