Co-ops differ quite a bit from condos. Let's focus purely on the financial requirements necessary to pass a co-op board. The first thing you should absolutely know is that policies and requirements differ from building to building. The 'general' financial requirements are:
1) A buyer should have 2 years worth of mortgage and maintenance payments left over in LIQUID ASSETS (cash, stocks, bonds, etc....) after the downpayment.
2) A buyer should have a gross monthly debt to income ratio that does not exceed 25-30%. (Stay closer to the 25% mark, and you will be better off.)
3) Good credit.
I just want to reiterate that these figures vary from building to building. Some boards (particularly on the Upper East Side) may require you to purchase the apartment outright with cash and possess a net worth of 5 times the value of the apartment. Other boards may require that you have post down payment liquidity that exceeds 2 years of mortgage and maintenance payments. Understand that meeting a building's financial standards does not equate to an automatic approval. You must complete a fully detailed purchase application (otherwise knowns as the "board package") that includes such documents as: all bank, brokerage and retirement statements, tax returns, employment letter(s), and personal and professional reference letters. The preparation of this package is key and will determine whether or not you are granted an interview with the co-op board.
Work with an agent who is familiar with the co-op process and has vast experience with board package preparation. Be sure he/she is clear on the board's requirements before moving forward, and for your own sake, gain an understanding of the process prior to jumping into a transaction. The last thing anyone wants is a board turndown after going through a 3 month process. Good luck!