Insurance and proper training are the baseline worth confirming first, a company should be able to speak clearly to both without hesitation, since it directly affects accountability if anything goes wrong during a job on your property.
Clear, fixed pricing before work begins is another genuine indicator of a well-run operation, vague quotes or pricing that changes significantly on the day are common signs of a less reliable service, while an upfront fixed quote suggests a company confident in accurately scoping the job.
Finally, it's worth checking whether a company documents its process, a documented completion checklist and some form of quality check before the crew leaves site suggests a business built around consistent results, rather than one where quality depends entirely on which technician happens to be sent out.