That changes a few things. Though some lenders will be fine with less than 20% down + PMI, nearly all boards (as I had mentioned) want 20% minimum, while many of them want to see a healthy cash reserve in the bank so they feel comfortable with you (this is why I mentioned leaving your 25k untouched). Not to mention, boards interviews could be like a night out with friends or a tribunal of gestapo officers. Much of it depends on those men and women siting on the board. They will look at your financial history, housing references, job stability (60k is good, but if you started 2 months ago, it may not hold as much weight as a lower paying job you've held for years), character, etc. You're credit, at 770, should be cake. it's also how much they like you, a sad truth. You could be a great candidate for one board and hated by another...a major downside in co-ops. At first glance, you may seem like a good candidate. However, don't forget boards will dig deep! It's difficult to predict how groups of other people think.
The Upside: Have you heard of a sponser co-op? They're great. Basically, they are co-op apartments held by a "sponser". See: http://www.wallfly.com/review/manhattan_ny/glossary.php#s
They typically have a transfer fee/tax, but are exempt form board approval (if you buy a sponser unit, however, and choose to sublet/sell it later, the renter/buyer will then be subject to board approval). They aren't everywhere in FH, but not necessarily uncommon, either. My first apartment purchase was a sponsor. It was a breeze...no board, no hassle, just a 2k transfer that the sponsor agreed to split.
Anyhow, either way, if you have strong finances (less than 20% down, unfortunately doesn't put you in this category with most boards), good references and don't seem like a shady character, a board generally will vote in your favor, barring any other exigent circumstances, of course.
With your salary, you shouldn't have too much problem qualifying for a mortgage given you don't have other massive debts that take a chunk out of your net. I see you have a great credit score, that's great, too. As far as down payment goes, if you're looking to use the 30k only and preserve your other investments, that will unfortunately not be good enough for 20% down, which is not only what the majority of co-ops around here require, but the lenders themselves to prevent you from paying mortgage insurance (PMI). If you don't mind paying PMI, or want to put more down (I wouldn't completely deplete your savings if that's all you have) You could find a quality 2br in FH/Rego Park for well under 275k. A few in my complex recently sold in the neighborhood of 250k. Nothing incredibly fancy, but spacious, safe, clean and in well cared for. They go even lower than that, but don't forget you get what you pay for. Hope I helped!