Apple Salesman.
Hi ours de gingembre. We will sort you.
Find a comfy chair.
OK, firstly, USB modems, generally, suck. They sometimes need drivers geared to your PC / operating system, and thus have an extra layer of 'fudgability' / 'klunkiness' / 'krud' to go wrong IYSWIM.
My initial suggestion then (not terribly helpful, I know), is to get a cheap, Ethernet ADSL modem. Tiscali may sell them all set up with your password etc. (on the other hand, they are rather big and somewhat crap so am not sure their customer service would extend to this).
You could try www.dsl-warehouse.co.uk/ . You would want a single port unless you want to connect additional computers (in which case go for multiport).
If your Mac has a wireless card, or you wanted to set up a wireless network in your house, now would be a great time to be a wireless ADSL router.
I'll press post and go google your existing equipment and come back in a tick.
FWIW - a small, friendly, national, technically clued up ADSL provider is Andrews & Arnold - they will sell you a cheap router with your login / password pre-loaded so when it gets to you it will be plug and play with your mac.
PS - Congrats on your Big and Beautiful new toy. May you be blessed with hours of happiness together.