Essentially there isn't enough information for anyone to answer your questions (unless they happen to be familiar with your system). Regardless of whether you don't like technical terms I'm afraid there really is no alternative to your telling us more about what you've got and what you're trying to achieve.
Sorry, I don't understand
and only because BT sent one of their usual arrogant "customer focused"...letters...I have decided to aquire a new PC and thus Win7
What do you mean by this?
Your questions:
(1) What modem? (Different setups will have different answers.)
(2) (a) Data files you can just copy using whatever means suits you (floppy, memory stick, network cable, etc etc) (for program files see (3) below). Whether the files are any use or not on the new machine depends on whether you've got an application that can read them (also see (3) below). So, what sorts of files?
(b) Emails you can only transfer if you're moving to a compatible application, so you'll have to tell us what you're using on the two machines. If it's Outlook Express on Win98 you could be a bit stuffed on Win7 as it isn't supplied any more.
(c) You could mean almost anything by "favourites", and the answer will be application specific. So what "favourites" did you have in mind?
(3) You won't (in general) be able to copy applications, you'll have to reinstall, and you'll have to install newer versions than you were running on Win98, which means you've got to go out and buy them. What applications are you using?
Good luck with getting a new PC set up over a weekend, by the way. When I get a new one I tend to have to run the old one and new one in parallel for about six months until I'm absolutely convinced that I've copied everything I need and that there's no rarely used tool I've not got round to setting up on the new one.