I don't like prefab coops either for all the reasons you've probably heard. They are usually not well designed for chickens, usually do not hold nearly as many as they say they will, usually have pretty poor ventilation, and the quality is often not that good. They can be pretty expensive. Still, a lot of people buy them and use them though many require some modifications. While a prefab coop may not be great it might be good enough for you.
Try to put a link to that site on here before you commit to buying it. If I see it I'll try to give an evaluation. You are in New York (thanks for that info) so your winters will be pretty rough. Although you are only planning for three they will be locked in the coop by weather a fair portion of the winter. They need more room than people with milder weather.
You say you cannot build a coop but you may have to assemble that one. Are you prepared to do that? If so you may be better off getting a shed, either off Craigslist if you can transport it and convert it to a coop or get a prefab shed from a big box store and convert that. In any case, will you need a foundation for what you select?
Another thought is to pick a small coop design up in the "Articles" section and get a quote from a handyman to build it for you. You will almost surely get better quality and the cost may not be that bad compared to the prefab with shipping and assembly.
Hey y’all!
