How do I get the best offer? (The obvious question.)

I have only spoken to HR so far. They've trotted out very specific numbers, and I've said "right ballpark" but been non-committal on any specific number. Realistically, market data says the average is a good 10-15% above their high-end. I would at least want that. No idea if I want the job at all until I can talk about the responsibilities with someone who knows better than the HR person.

Do I need to push them this early just to get up into the right range. Or if they're within 10-20% of something I could accept if the position fits, is it that close enough to leave the numbers for later? They also asked about moving expenses, which, to be honest, I need. But I basically said, it's not going to dent your bottom line to give that, and I'm sure we can work it out.


Background:
I submitted a resume for a job I'm interested in through a friend of friend, not someone who will necessarily pull strings or give me the straight dope. I lack a true insider. He and I exchanged a couple of emails, then I was directed to HR and department that is hiring.

First contact: call with HR, about 45 mins, all very positive. Talked about a lot of things. Then set out basic salary info [numbers are totally made up here, but percentages are roughly accurate]: "we're thinking 75k-80k, maybe 85k for a true all-star and could maybe go higher than that. Plus 12k of restricted stock, vesting over three years". I said 85k could be in the right ballpark, but I'd need to look at total package. Liked what I'd heard otherwise. Scheduled a second call.

Second contact: another 45 min call with same person from call. A series of scripted questions that I answered. Reiterated same numbers as above. I said basically "75-80k would be a clear no, 85k could be in right ballpark, but depends on the whole package". Talked about benefits, they'll send benefits info -- 401k match but only after first year. Set up third contact, finally talking to person in the department.

Third contact: two days from now.