I was recently working with a first time home buyer, and we looked all over Manhattan. I took him to several UWS studios. We were looking for approx 400sf or larger, up to $300,000 price.
If you can live in 300sf apt, my colleague has a MINT, studio with a very large kitchen that has some of the best studio finishes I came across. Typical Maintenance will be between $600 and $750 on that size and prices will be in the area of $265,000 to $300,000. If you go lower on price you may need to do a large remodel job.
Your issue will be the following. Debt to income Ratio. What kind of debt do you currently have, maybe some school loans? Would your parents step in as guarantors or co-purchasers?
If a coop doesnt feel you are strong enough they may ask you to put more money into an escrow account in case you default on your payments. Debt to income shouldnt really exceed above 28%, but some buildings have other preferences, you will need to know that beforehand. If you will be looking at this as an investment, try to look for buildings with flexible sublet policies.
Good luck Caterina, and don't hesitate to ask more specific questions.