Okay, different field, but still applicable:
I am looking for contract and per diem work as a nurse. I am mid-profession, highly competent, and should be able to command a mid to upper range rate of pay. However, my last position, where I spent several years, was paying me close to what they pay new grads. I had been too loyal to an organization that gives pathetic raises (1%), and that has a reputation for paying poorly. I had my reasons for loyalty, but it was extremely expensive in terms of wages that I could have earned elsewhere.
There are positions for which I am qualified that were recently advertising rates up to $45/hr (plus benefits, 13 week contract). When they heard what I had been making, they tried to offer me a rate in the low 20's. I compared notes with another nurse who was quoted a lot more than me. She was less experienced, but her last job had been paying her better. I held my own, explained that I knew my worth, and the offer went up close to the top of the range. That would have been acceptable, except that once I checked out the job, I realized that they couldn't pay me enough and I declined the contract.
This is business. You don't have to worry about hurting someone's feelings by asking for too much, or try to be "nice" by asking for too little. Everyone wants the best possible deal they can get. They want to pay the least amount possible for the best quality, and you want your paychecks to make you feel great about going to work.
If you see a range and say that you are willing to work at the bottom of it, you aren't going to be offered a place in the middle. Consider what salary you would be happy with, where you would feel that you were being fairly compensated for your work and that your value to the organization was being appreciated. Then add 15-20% or so to that figure and ask for that. It is reasonable to negotiate salary, and you need to have some room to give up ground without ending up underpaid. If they accept your number without any negotiation, that is a sign that you probably left some money on the table and could have asked for more.
Check out Glassdoor and Salary.com for some real figures on what others like you are getting paid. Don't ask for the minimum you would settle for, because that is probably what you will be offered, or some trivial pittance above it. HR folks will try to sell that number as "just what we are offering," as if they have no discretion. Rarely is that true. And if it is, it is better to walk away from a job that doesn't pay you decently, so that you can be free to find a better offer down the road.
The rate you get for your first job is important. Subsequent employers will look to your salary history as a relative measure of your worth, and if you set the bar low to start, it is going to cost you tens or even hundreds of thousands of dollars across your career.