AndrewC: Unfortunately I don't think Adobe AIR will help you too much with the multiplayer aspect as you'd preferably have to write your own server stack/software to handle all the data. It will help you with transmitting data to and from, but not anything else.
Even with XNA/C# you'll have to do most of it by yourselves but at least there you'll get hands on experience on actually working on it and it'll get you familiar with a language that is used almost everywhere (or different (sub)sets of it).
You could also start with the free portion of Unity which can be found
here or even with Silverlight for something more of a challenge.
barjed: Yeah, I was aware of the online component. I am also thinking about the graphics, though. I just think that XNA _might_ be an overkill for a game that will consist mainly of a lot of interface, plus more interface, plus some sprites :P
As I said, I am an ignorant when it comes to games. I would very much like to avoid C++ though, as it is something that makes me wake up in the middle of night screaming blasphemies and stuff like that. Don't ask me why.
The platform independency is not that important as the general idea was to have something that resembles a crossover of Final Fantasy Tactics/Tactics Ogre/Disgaea (I mean sRPGs in general) with HoMM, where the source gathering, building etc. is played like a browser game through through the browser (obviously) and the battle component is where the game plays like a normal game.
The nice part about XNA is that it allows you to easily port your game to the Xbox and handles a lot of things well (Flotilla was made using that and is a great little game). Combine it with a great (imo) programming language (C# that is) it makes for fun things.
Also, I always considered it to be better to have a challenge/build something overkill while learning than to have to do it while actually being paid to.