If you buy the car before the move you can title, register, and insure it in CO. After a few months if the move to NY looks like it will end in a few months then just keep the car registered in CO. If you plan to buy the car in NY sometime after the move is made, then you will find it easiest to title and register it in NY. To buy and register the car in NY you will have to get a NY driver’s license first, then register the car.
The biggest issue is paying taxes and fees. If you buy the car in CO you will pay sales tax to CO. When you move to NY you need to know if they charge a fee based on the car’s value? If they do then in effect you are paying sales tax twice which is a chunk of money. Many states have “value” fees associated with titling and registering a car in their state, NC and SC and many other southeastern states have these fees. I’m not sure about NY.