If cheat-resistance is a must, I suggest that all the game functionality is on the server. On the client side, you could just use plain HTML with a number of buttons, which would cause the server to take the appropriate action and regenerate the display. If you want a more sophisticated client look, then java could be used to display the cards on the client. However I suggest that only data that the player can legitimately see is transmitted to the client.
The disadvantage of using Java on the client is that not everyone has Java installed. You can get the browser to fetch it using the <OBJECT> html tag, but this still requires a 15MB download - fine for broadband, but not for dial-up. It might be possible to do the client using Macromedia Flash, which has a wider installed base. I don't know whether Flash has sufficient functionality for your application, but I think its worth a closer look.
The server side is where the bulk of the work (and cost) lies. You will need a fast server side program to do the donkey work. Scripted languages such as PHP won't really cut it here when many players are involved. Either you need 'shell' access to the webserver, in which case you can write the server application in C++, or you could look at web hosts specialising in supporting Java Servlets. I suspect the second choice would be cheaper from a hosting point of view because you have less access to the server and thus less chance of screwing it up.
Servlets can also be used in conjunction with Java Server Pages (JSP) technology to provide back-end services for a webserver and might also be a good choice, if you decide to use HTML only on the client.
Costs are a bit of a grey area. The client isn't too complex and could take anywhere from a week to a month to write depending on the complexity. Most Java or Flash programmers could manage this. You may want to employ an artist to do the graphics. The server is likely to be where the complexity lies, particularly if it has to handle billing (you didn't say), in which case linking to a site providing card transaction services is required. You would need to consider security pretty seriously if user card details are stored on your server. I have no idea how to do this and suspect that those with the right knowledge won't be particularly cheap. Here be dragons.
The other issue, if this is a commercial proposition, is to determine the extent of the market and figure out how to draw the happy punters to you site. Some of the freebies I have posted on this site (only) have had several hundred downloads, but I doubt that many of those would have converted into paying customers (even if my product was better). I guess notifying magazines of your product and some modest advertising would significantly up the throughput. I see you're in marketing, so hopefully you've got a handle on this
That sadly is the limit of my knowlege.