The Tiscali Emails you have already got in Outlook will stay unless you delete them. The actual Email address from Tiscali will terminate and you will no longer get emails from Tiscali or TalkTalk servers.
If you get a new BT Home hub then its a simple case of connecting it to you computer via Ethernet/Lan cable. If you old Tiscali broadband was using a USB modem then you would need to uninstall this and also uninstall any tiscali software listed in Add/remove Programmes.
BT Broadband one connected via Home Hub (Usually Black) just needs plug-in and wait a minute or two for it to wake up.
You do not actuall need to run the software BT provide but you can do if you want BT Yahoo Broswer software which I have found to be a system hog over the years.
For Email you could configure BT Yahoo Email to work in Outlook but I would have to go and find settings for you later.