I agree with Nathan (don't forget to price running extra water, sewer and electrical lines).  

Getting that first property is exciting—and yeah, NYC is no joke when it comes to price of entry.Honestly, a lot of people I’ve talked to in your shoes end up finding better opportunities just outside the city.

You won't find a great software for free or a low price.

Landlords mistakenly ASSUME all PMCs offer the exact same services and operate the exact same way, so price is the only differentiator.So, the first question they usually ask a PMC is about fees - instead of asking about services.This also leads them to ASSUME simpler is better when it comes to management contracts.

The document that records the sale is called a "Tohon" and does not list a sale price. 

You can present an offer that aligns with your financial goals, but be prepared to walk away if the seller won’t negotiate to a price that ensures you’re not left in a tough financial situation.

Is there some reason the early bird pricing went up without a deadline and without warning?

Quote from @Frank Pyle: You can refinance with conventional but value of property for LTV purposes will be capped at purchase price plus documented upgrades for the first 12 months.  

That said most folks have price targets and if large complexes are conceding 1 or 2 months on the 1st year lease, itll put downward pressure on your rent to some degree. 

As @Jonathan Greene mentioned this is kind of a dated strategy in the new price/interest rate environment.