Gymtime, you can use Norton Ghost or etc to copy the disk image over. I also like to copy the Windows CD "WIN98" directory over to the HDD before I make the move, incase the CDROM/controller doesn't work right if you simply move the old HDD over. Since those are moving parts items though it would be wise to image to the new system, although then you'd probably be stuck with your current OS instead of the fancy pants WinXP Home or whatever you end up gettin that is newer, plus you'd have to instal new drivers etc.
As for moving Outlook Express there is a directory you can simply copy over, if your on 98 its somewhere in C:\Windows\Identities (frig, rusty memory, if you look under File > Properties in OE after highlighting an email folder it will show the dir, on 2k mine looks like C:\Documents and Settings\Administrator\Local Settings\Application Data\Identities\{xxxxxxxxxxx-4411-9EB0-xxxxxxxxxxxx}\Microsoft\Outlook Express\Inbox.dbx ), if you rusing Outlook regular just look for *.PST on your hard drive, and move them to the new system or do an actual 'export' formally of your address book/email etc
As for modem setup and stuff that is all going to be setup unless you buy in parts, which I do. As for your ISP etc though yes you will have to move that stuff over settings wise. Keep the data on your old drive and move it to the new machine to suck stuff off of it, then setup your ISP and etc, and put the old HDD back in the old machine and give it away if you want.