You need to understand the buying process on this side of the pond is very different with respect to the role played by the professionals. The UK is almost unique in not requiring estate agents to be licensed. Here and in most other parts of the EU, agents must be licensed. In some US States, agents can handle everything, there is no lawyer involved. New York requires you to have a New York Licensed attorney involved. Nevertheless, please understand that the legal responsibilities taken on by the attorneys here are significantly less than solicitors in the UK, so it's very important for you to be working with professionals here that have a thorough knowledge and experience of the differences and international sales.
I see that other agents here are saying that they are not licensed to practice law, only real estate, and therefore cannot give you legal advice. This is absolutely true, but what they are not telling you, because they may not know (and I wouldn't expect most to know) is that their license permits them to carry a lot more of the legal responsibility in the transaction than their UK counterparts. You may know that already, but if not, there is a huge area of confusion already about who is responsible for what in the transaction. As a professional in real estate in first the UK, then the US for more than 20 years, I have that T shirt!
New York Real Estate law requires agents to disclose to the buyer who they represent in the transaction, so the safest way for you to proceed is to ask whichever agent you decide to contact for exclusive buyer representation. This means that if you see a property you like, you do not go direct to the seller's agent because they are already signed up to represent the seller, then all they can offer is a dual agency arrangement, whereby they represent both of you in the transaction. I suggest that's not good enough in your situation.
It is absolutely NOT the case that "he who pays the piper calls the tune", in real estate here. On the contrary, it is very common for the buyer's agent to be paid by the seller's agent at completion of the deal, they split the commission between them. What you want is an arrangement whereby your agent will be required to be 100% loyal to you.
One tip I will share is to pay attention to the insurance you will need for your property earlier rather than later. UK insurance is very very different, and you will not be able to complete the purchase without insurance if a bank is involved (and I wouldn't advise that you do anyway even if you are buying cash). Unlike UK building policies you may have, your US policy will only have limited Liability cover, (slip and fall etc.) . Because of anomalies between the two systems, and depending on the value of your personal assets in the UK, that may not be nearly enough, and you will then need a custom solution from an insurance agent who again, understands the international issues.
I have various other people I can put you in touch with if you contact me offlist, including a British Accountant in Manhattan, who you may need to consult regarding tax implications if this is going to be a investment property, as you would then be subject to the dual taxation rules for income derived from rents.
By now, I have probably put you off the whole idea! Please don't be, you are very smart to think about buying here now - it's a great time to do it and not that complicated if you have someone to walk you through it who is on your side. If it's a buy to let you want, also consider the Hamptons and North Fork, in Long Island Wine Country, because it is a resort area with vacation rentals, only 2 hours from Manhattan. That's my area, whereas for Manhattan, if you get replies here from people with the necessary expertise, You would be better to deal directly with them. Otherwise, I would be happy to refer you to my contacts there.