AppleScript string constants can be no longer than 32K. If you need a longer string at compile time, you can concatenate multiple string constants with the & operator. Of course, you won't run into that limitation in Script Editor, because it can't edit scripts whose text is longer than 32K. As far as I know, there's no limitation on string size at runtime other than that imposed by available memory... and there's a lot of that to go around if you're running on OS X.
Numbers automatically transition from integer to real when necessary to preserve place value (precision? who needs it?). Not sure what the biggest floating-point number you can have in AppleScript is, but it's probably well into the 10 ^ 150 range.
Lists and records have no limit that I know of.... though now that I think about it, it might be limited to the maximum integer value in AppleScript (which is somewhere around 5,000,000), since it has to use integers to keep track of list elements.