I plan to make an pretty big application on Facebook. Would it be a wiser choice to get the code working on any hosted site before actually modifying it to be used in Facebook? Or would it be too much of a pain to make the code compatible with Facebook?
It depends on how you implement the Facebook integration. If its a Canvas app, you can choose between IFrame and FBML. If you go with FBML, you'll have to have to register the app with Facebook from the start since it uses Facebook specific XML. If you go with IFrame, you can do everything but the Facebook integration without registering your app. See http://wiki.developers.facebook.com/index.php/Choosing_between_an_FBML_or_IFrame_Application for more information.
There may be other options for a Connect app, but I have no experience with them.
What platform do you plan on using? There are Facebook APIs for javascript, PHP, and .NET.