Theoretically it looks like it should be a slam dunk, however, that's not how it works and you will have problems:
1. If you have 60 - 85% saved for a down payment, how are you paying the remaining 15 - 40%? If you need a mortgage loan, understand that lenders refuse to finance loans under $100,000. A few will go down to $80,000. but it will be difficult finding a lender to give you a loan for a co-op below $100,000.
2. Condos are more expensive than co-ops. Have you been pre approved yet? What is your budget that you can afford? This will either limit you to co-ops only or you can afford both.
3. In New York City there are many more co-op buildings than condo buildings.
4. If you are buying a co-op, you will need to be approved by the co-op Board. One thing they will insist on is a full time job with an income that is sufficient to pay the mortgage + the maintenance fee + utilities. Co-op Boards will not accept a buyer who will get a job with a higher income down the road.