Who will actually be in my house, and will it be the same person each time? This is the question that predicts the most about your experience. A consistent cleaner learns your home and your preferences; a rotating crew starts from zero every visit and you end up re-explaining the same things forever.
Is this a flat price or an hourly rate? Hourly sounds fair and usually is not, because the incentive runs the wrong direction and you have no idea what the bill will be until it arrives. A flat price for a defined checklist puts the risk on the company where it belongs.
Can I see the checklist before I book? A cleaning service that works from a written room-by-room list can send it to you immediately. One that cannot is going to define a good clean after the fact, which is exactly when disagreements happen.
What is the difference between your regular clean and your deep clean, specifically? Ask for the extra tasks, not the extra hours. If the deep clean is just the regular clean with more time on it, you should know that before paying deep clean rates.
What happens if something is missed? The right answer is a clear window and a return visit at no charge. A vague reassurance is not a policy, and you will find that out on the day it matters.
Am I locked into anything? Recurring cleaning should be a rhythm you can pause, move, or stop. If cancelling costs money, ask why the service needs a penalty to keep you.