Is this the only job you are interested in? Do you have a best alternative to a negotiated agreement (BATNA)? Usually a BATNA, in this situation, is a job offer from another company that you have time to respond to. Sometimes a BATNA is another situation. You want a job, but you'd also be OK taking a year off and backpacking, so the offer has to be worth it to keep you from doing that.
When I got my first job out of college, I basically wanted any job. I came in under market. I didn't have any alternatives. My previous wages had been really small. That's the problem with entry-level jobs.
You're not at entry level. You are trading up and you are looking for a company where you will be respected.
It can be perfectly okay, in a negotiating situation, to tell them your current/previous salary and your almost, but not quite, ludicrous salary expectation. It can also be okay to hold that to your vest. They will assume your previous salary is low, but they won't know how low.
No employer will hire the discount candidate over the best candidate. They want to hire the best employees and get them at a discount. If you aren't #1 on their list for every reason other than salary, they will make an offer to the person who is. If that person is out of their absolute price range, they will move to #2.
If you come in with a low salary expectation but they think you are awesome, they might get scared. Maybe you are awesome but you are being edged out of your company because nobody can work with you. Or perhaps you have a tendency to harass other employees.
Ask for the highest number that you think won't get you thrown out of the room. Make them bring you down from there by offering you concessions. More vacation time? Guaranteed training and conferences? If it's a private company or a zero-earnings company, stock options are not a concession.
If you are offered stock options, ask to see a financial exhibit, so you know what you are being offered. If it's a public company, you can look at their SEC statements.
But if you don't have any alternatives, you won't feel comfortable holding out. So make sure you work your other job offers. And if this is not your #1 choice, make sure that you have plenty of time to make a decision, so you can incubate other offers.