First is have them review the project. Ask if there is something that sticks out. I have seen " wish " plans whereby the city approves and architect plan producer write things in that are not possible or cost prohibitive.
You should have a solid plan from outset and avoid change orders. A good GC will be able to distinguish this from a quick review.
Ask how they bill change orders. Even with a perfect plan unforeseen things happen. Nobody can see underground or inside inaccessible building cavities. How will they be handled?
For some change orders are an opportunity to gouge and a huge profit center. They happen and often. How they are handled can make or break a budget.
Availability as asked above is key. I would disagree in comment that if someone is available that they are not good. However make sure they have time to start and complete your project.
Run a license check to see if they have formal complaints. It normally has to go pretty wrong before a formal complaint is logged. If there are multiple a big red flag. If there is only one ask it could be a customer that is problematic.
Get an accord doc that has their insurance information and review to make sure it is adequate for your job. Ask how long they have been with their agent. A good contractor will not shop yearly fore insurance to save coast. They will stick with someone with a good price and excellent service. Are they willing to add you as additionally insured. This is a simple phone call to agent and should not be a cost add on.
Ask for a vendor list. If they are only using big box stores I would think they are inexperienced.
Ask for a contractor list and check them out as well
Use social media yelp angies list to investigate reviews. Can be unreliable as some folks just complain and not everyone uses those. But if there a multiple bad reviews of the company and or listed subs could be a red flag
A schedule of payment underground completed concrete completed x dollars framing completed x dollars rough in x dollars. etc These are considered complete ready to pay when signed off inspection card. Large downs are unreasonable. Its your money make sure they earn it. Landing material and a payment is also reasonable make sure it is signed off as such when paid.
Make sure they are in their field of expertise. Residential and Commercial are very different. Remodelers vs concept to completion are very different. Make sure the contractor fits your needs.
Make sure you like them as you will be working with them. Adversarial jobs are a nightmare.
Best of luck