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Well thats a good question. One of the most widely used frameworks is express.js, but it all depends on your API and if you want to build anything else, I mean besides API you want to add 1-2 pages.
Another option is restify.js, its an old player on the field and is very similar to express, except it does not have template support. If you only want REST API in your app, then restify should be a good selection
Choose tool with the biggest community. So it is ExpressJS! You can find a lot of guides and tutorials for it how to build Restful API with it.0 likes
to find the best framework you have to try few of them and see what works best for you. the word "best" is personal. what works best for me may not work best for you. and "best" can have different meaning for different people.
for example i am happy with using just connect JS and keeping it light weight. Some prefer to bring a swagger based framework to provide a better UI for those who want to play with the API. Some can be hardcore and just build their rest stuff using just plain http. Hope this helps.
I think ExpressJS is kind of a popular choice for it. That being said, there's probably no 'best framework'. All of them will have their share of advantages and disadvantages. You take what you feel comfortable with and be done with it.
It is generally a good sign if the framework follows common best practices and principles in software and that is easy to debug (if following best practices, this should not be a problem, should it ;) ).
@Techly: You might want to check Lumen (a micro-laravel) or Slim. Lately I've found myself spending a lot of time on PHP and... well, not my favorite language, you can be sure. The above paragraph applies to this as well.