Here's the problems you face:
MP Plugin: While this is probably the easiest solution to implement, it requires use of the signalling server. If it ever goes down, you game goes down. It also means your clients are connected to each other and none of the data or stats are funneled through any service you have so collecting that data requires additional work. It can act as a server but this requires that somewhere on the internet you have to have a dedicated client running inside a browser. To me, that's just a huge, huge overhead for running a server. It just seems silly, though I suppose it does work to a degree, to have a server running inside a browser. And, that also means that if you're going to host the game on fast commercial connections, you'll need a server that you can VPN into to constantly make sure that browser is running.
Ajax: Connecting to a webserver with Ajax is easy enough. You'll have to write scripts in a language like PHP to make requests of the server. The problems here is you're only making requests, it's one way communication. The server can't 'push' notifications out to your clients using just Ajax. Your clients can 'poll' the server with a request, say every second, and see if there's anything it needs but this has it's own set of problems. You get 1,000 clients polling a server every second and you're likely to run into hosting issues.
Web push notifications: There are methods out there to send these 'push' notifications to clients and I have successfully made them work in C3. However, each such connection to a server becomes a constant connection. Unlike Ajax which makes a brief connection and then disconnects, this method keeps the connection open. The problem there is, each client is going to need a connection and to get more than say 100 connections on a web server, you're getting into premium server price range. You get more than 1,000 connections and you're going to need some server horsepower to manage them all.
WebSockets: This method has the potential to have thousands of active connections without using the actual webserver (like Apache). Many games use this along with other communication methods (UDP/TCP) to communicate with clients. The problems here is that you are going to have to write a dedicated server in, most likely, a higher level language like C#, Python or C++, which can be a daunting task. You'll also need hardware sitting somewhere that the server code can run on.
For a card game, lag shouldn't be an issue. Were I thinking of doing something like this I'd most likely look into using Ajax or a combination of the MP plugin and Ajax to collect stats from the players.