Having just completed an app involving lots of nginx reverse proxying, I would be more inclined to go with either your second or third option. ...or maybe something slightly different. Lets break it down to individual points to consider:
Static Files
For serving static files (for either the website or the app), node and nginx are the clear choices as they don't fork themselves for each new request like Apache does. Node is faster than nginx at serving static files, but depending on the amount of traffic you'll see, this might not be a meaningful difference.
I would choose nginx as the public-facing server and reverse proxy requests to other things as necessary. Even though it is slightly slower than node at serving static files, its flexibility and ease of configuration make up for it. PHP, if you choose to use it, is faster (configured properly) with nginx than with Apache, and nginx's configuration files are similar to Apache's but more concise. It shouldn't be too foreign-looking when you dive into it.
SSL
If you are planning to use SSL, save yourself the trouble now and get the latest version of nginx so that you can utilize the latest version of Google's SPDY module. Currently, the latest version is 1.7.3. Some package managers are behind quite a bit, so you may have to compile from source. If this is the case, make sure that the --with-http_spdy_module --with-http_ssl_module flags are used, among others. Here is a guide for that as well as setting up the configuration files to use SPDY.
Because all your requests go through nginx and a single domain name, you only have to set up SSL in one place. Any reverse proxied requests do not need to be over HTTPS because they happen internally. If you make node.js run your app, you just have to make sure it only listens on localhost and doesn't serve external requests directly.
Application
Node is a good choice for the application code and the long polling that you wish to accomplish. It is also fairly straightforward to proxy these long polling requests through nginx. With these two nginx options...
client_body_timeout 1m;
client_header_timeout 1m;
... you can adjust the timeout of requests. You will want to make sure your application code puts an end to the requests before nginx does. Otherwise, you will get a 504 Gateway Timeout instead of a 200 ok. If the nginx timeout is set to 60 seconds, you should end and restart a long polling request every 55 seconds or so.
Website
If you aren't set in stone with using PHP, node.js or a static site generator written in node.js could also work for your needs. Docpad is one that I use, but there are many great options. Node packages like Grunt make deployment automation easy. A few of the things I use it for are HTML, CSS, and JavaScript minification and cache busting.
Best Answer
I think it is useful to do this.
nginx has a lot of code to shovel files efficiently from the disc to the network socket in a non-blocking way. It does this much more efficiently than node.
Of course, if you're not doing much static content serving then it might not be useful.
But nginx can also load balance over multiple node servers, so that's another potential advantage. Your app has to be written to be scalable like that though.