If you must start with a number, Ask for what you think you're worth x 2 and work backwards from there.
Don't count on people just accepting your monetary value simply because they should.
2 jobs ago, I was worth 65k/year. One year later I'm worth 135k/year.
Did my skills double in that time? No. They did not. My bargaining skills did increase though.
Ideally you want them to reveal their number first. If they won't, you can suggest that you each write them down on a piece of paper, and then swap pieces. If they won't even do that, give them a number that you'd be delighted to receive.
Note well: I think this is sound advice, but I have not tried it. Use at your own risk.
The short answer is you shouldn't ask for anything. It's in your best interest to keep both your desired and current salary to yourself and to let the company make you an offer. That puts you in a better negotiating position and has the benefit of answering your secondary question of "What is the current market rate for new grads?"
Sites like GlassDoor.com, payscale.com, and salary.com are good for getting averages and doing research (see below for a note on this), but the best way to find out what a specific company will pay a new grad with your skillset and experience is to let them tell you by making you an offer.
Instead of telling them what you want to make, focus on demonstrating your value and competence throughout the interview process so that the company offers you a salary that's at the higher end of the range they're prepared to pay someone to do the job you're interviewing for.
I see someone also recommended patio11's blog post on salary negotiation—you should absolutely read that (it was a big inspiration for my book). Here is the link in case you missed it: http://www.kalzumeus.com/2012/01/23/salary-negotiation/
One last note on researching your market value: You should absolutely do that research because it will inform how you respond to the offer they make you. Getting the best possible offer is the first step, and then you want to work to maximize your salary by negotiating effectively.
http://www.kalzumeus.com/2012/01/23/salary-negotiation/
It gives you the right mindset for the negotiation.
If I were you, I would ignore salary negotiation, and consider employment in terms of learning opportunities and getting right experience.
I've hired a lot of sys admins and ops people and most undervalue themselves.