You should never ask them for a budget- because, as you said, they have no idea.

Your first consultation with them should be to discuss the various options, show them pictures of similar projects to what they are after, and YOU should be telling them what these things cost. Then, you say "based on what you are telling me, a system to deliver what you are after is going to cost about $X". Then, you shut up and let them talk next.

If their jaw drops, then you have just found out that their budget is much less than it should be, and you can part ways without spending any more of your time.

If they are comfortable near the price you specified, you can collect your deposit and start engineering their system.