The three questions that matter most are: who owns the website when it is finished, what happens after launch, and who is actually doing the work. If you only ask three things, ask those. Every expensive mistake I have seen a business make with a developer traces back to one of them being left vague.
The rest of this is the longer list, with what a good answer sounds like. None of it requires you to know anything technical, which is the point. You are not assessing their code. You are assessing whether this is going to be a reasonable working relationship.
The three that matter most
"Who owns it when it is finished?"
The answer should be you, unambiguously: the design, the content, the domain, and the code. You should be able to leave and take it.
Warning signs: the domain registered in their name rather than yours. Code they describe as "their platform" or "licensed to you". Any answer that treats the question as unusual, because it is the most normal question in the world.
The single most expensive situation I encounter is not an overpriced website. It is a business locked out of its own site because the person who built it stopped answering, and nobody can find who owns the domain.
"What happens after launch?"
Some quotes end at launch. Some include a period of updates. Some include nothing and bill hourly from day one. All three can be fine. Not knowing which one you bought is not.
Ask what a small change costs six months later, and how long it takes. The specific number matters less than whether they have one ready.
"Who is actually doing the work?"
With an agency, the person selling you is often not the person building, and things get lost in the handoff. With a freelancer, they are the same person, which is better for communication and worse for capacity. Neither is wrong. You just need to know which you are buying, and if it is an agency, ask who your point of contact is after signing and whether that changes.
The rest of the list
"What does it start at?" A refusal to give any number is a sales tactic. Scoping genuinely is needed for a final price, but a starting point exists and they know it. Mine are published: $850 for a landing page, $2,900 for a small business site, $4,800 for ecommerce, and the full list is public.
"What is not included?" Better than asking what is included, because that list is marketing and this one is not. Copywriting, photography, ad spend, plugin licenses, and ongoing content are the usual exclusions. They should be stated without hesitation.
"Do you mark up third party costs?" Domains, subscriptions, plugin licenses, and payment processing should be billed to you directly in your own accounts. A markup on a recurring cost is a quiet annuity you will pay forever.
"How long, and what makes it take longer?" A real answer has a condition attached. Mine is two to four weeks for a small business site from the point I have your content, under a week for a landing page. The condition is the important half: content is the single most common reason projects stall, and a designer who does not mention it has not run many projects.
"What do you need from me?" If the answer is "nothing, we handle everything", be suspicious. Good websites require your input on what the business actually does. What they should be describing is a process that gets it out of you efficiently.
"Can I edit it myself?" Decide whether you want to. Some people genuinely never will and are better off paying for changes. If you do want to, ask specifically what you can change without calling them, because "you can edit it" covers everything from full control to changing one paragraph.
"What happens if I want to change something and you are busy?" This is the freelancer question, and a good freelancer answers it honestly rather than pretending capacity is infinite.
"Can I talk to a client you built for a year ago?" Not a recent one. A year ago, when the novelty has worn off and they have needed support. That is where you learn what the relationship is actually like.
"What would you talk me out of?" My favourite question. Anyone who has done this a while has opinions about what wastes money. A designer who agrees with everything you suggest is either very new or is going to build exactly what you asked for even when it is wrong.
What good answers have in common
They are specific, they include a number or a condition, and they sometimes contain bad news.
When I built TEXPEPS, a telehealth marketing site, a large part of the job was saying no to copy that would have been stronger marketing and an actual liability, because a non-clinical platform cannot promise clinical outcomes. A designer who will not tell you no is not protecting you from anything.
The three answers to walk away from
"Don't worry about the technical side." Ownership and hosting are not technical details, they are business terms. Anyone waving that away is either careless or counting on it.
"We guarantee first page rankings." Nobody can honestly promise that. It is not a bold claim, it is a false one, and a business willing to make it will make others.
"Unlimited everything." Unlimited pages, unlimited revisions, unlimited support. There is no such thing, the limits exist regardless, and you will find them by irritating someone. An honest provider states them up front.
One thing to do before any call
Write down, in one sentence, what you want the website to do. Get more calls. Sell a product. Stop answering the same question forty times a week. Look credible enough to charge more.
Most conversations about websites start with what it should look like, which is the least important decision and the easiest to change later. Starting with the job it has to do changes the entire conversation, and it also tells you immediately which designers are listening.
If you want to see how I answer all of this, the website development page covers the process and the pricing page has every number on it. Ask me anything on this list. I will give you a straight answer, including when the answer is that I am not the right fit.