it's hard to say, it's becoming such a specialised area that you should really focus on one side or the other, but if you do want to cover back and front yourself I would recommend coldfusion as it's the easiest to implement and since it's own by macromedia integrates well with flash, it isn't cheap though.

personally i use a LAMP (linux, apache, mySQL, PHP) set up, it's free and flexible. There is an excellent 3rd party AMF version of flash remoting called AMFPHP which is still in beta but is stable and usable, macromedia have tacitly endorsed it with articles on their site, also suggesting they're not creating their own version of remoting for PHP.

I would recommend learning java if you're starting from scratch, it's an excellent language with a lot of uses. Also learn XML if you don't, play around with XML servers, like moock's unity as they can be an excellent way of moving data around between clients/server.