I applied to a job, and when asked about a desired salary range I said 35-43 per hour without really doing my research. I looked again and realized that the job is listed at 75-85 hourly and to be honest, 40 per hour would be great. They emailed me back and asked again about my salary range. Should I change it to 75, move it to 60, or just keep it at 35-43 per hour?
Possibly, if you asked for 40 for a job listed 80, you may be a wrong fit for the job or underestimating the challenge it represents. If that's the case, there's still a possibility that another offer will fit your more in the same company.
Although I understand your wanting a higher hourly rate, changing your salary range from 40 to 75 would raise red flags, so I'd advise you not to change it as it might be seen as scam from your part.
Be more cautious with such offers in the future, but in this case I believe your best move is to keep your offered range. Maybe they'll give you more, maybe you can even ask for a raise after a little while. Don't change your offer.
I would not change my offer before meeting with the recruiter.
If you significantly change your offer, this will raise a lot of questions. You should discuss it during the interview process in face-to-face. It is very likely that the interviewer will ask you this question again, since you have asked for only half of the "normal" salary.
Start asking yourself the following question: Am I prepared to take this job for 40 hourly ?
Your answer seems to be yes. Then, anything above that is pure bonus compared to your needs and expectations. Even if the average internet answer is 80, you would be happy with 45. Additionally, this job might be an excellent start for your career, and you might get it because of your low salary pretentions. Go for it with your current range, stay coherent, and aim for the high part of your range (43) rather than the low part (35) if you have the option of discussing this with the recruiter.
On a side note, a very important question you should ask yourself is : why is this so highly paid ? Are you sure you have the qualifications for the job ? Is there no hidden negative, for instance night-hours or heavy stress ?
You've asked for roughly 47%-50% of what you say the job is listed at, making the assumption that it's a correct range, let's assume it is until you prove it to be otherwise.
This would raise a red flag to me if I were a recruiter. Someone who asks for way less than what's considered normal sounds like someone who thinks very little of himself or is either completely out of sync with current market values. Asking for a higher number is a hint of confidence and ambition.
If you're certain you got the skills for the jobs then there's no reason to settle for less than the other ranges you've found. If you don't have the skills you should consider going lower, but definitely not take a 50% cut. Take the lower part of the range if you're not confident enough to ask for the upper part but stay close to it if you think you fulfill the job requirements.
[...] I've come to realize that the range I asked for before is not in sync with today's market salary thus I'd like to ask for a salary in the range of X-Y. I believe my skills for the job match this requirement.
If they want you, they'll always make a counter offer anyway. I know people who have asked for a way higher number than what's considered "normal" for their level of experience and if that's the case they are simply told that it's abnormally high, and they'll tell you what is considered normal and will make you an offer in that range, if they truly want you.
It's hard to give you a number, since I don't know how fit you think you are for the job. If you know you fulfill all the requirements I'd ask for the range you found. If you think you're slightly lacking I'd not go lower than 65 as the lowest part of your range. Maybe they counter at 55 or 45, or even 40, which you say you'd love.
This way you'll in one way or another, through this company or another, receive a higher salary if you stick to market values, and the company that hires you will feel like they've made a better recruit by not picking up someone who does not truly believe that they are fit for the job.