For ADSL in the UK the two best ISP's are Nildram and Zen, pop over to
www.adslguide.org.uk for more information and users comments
Yep your Alcatel modem should work fine with whichever ISP you decide to use. If you go for a wires only service then the ISP wont supply any hardware
The D-Link ADSL Ethernet modem is about £68 and routers are just under £100, whether you should get one or not depends on how much your willing to spend and how annoying the logging in is