Anti-virus definately, also essential Firewall, such as Zone Alarm, and Ad Aware too. Keeping it on all the time is entirely up to you. I have all above with my BT Broadband, and I switch off several times each day, depending on whether I am home or not. Enjoy. btw, make sure you update Virus/ZA/AdAware daily.
There's a lot of rubbish talked about ADSL connections, and when broadband was relatively new I remember one forum member saying that he was leaving it connected permanently because "I'm paying for it, so I'm going to make sure I get it".
If you leave your connection running day in and day out you'll be sitting there on what amounts to a fixed IP address - it will be like a little flashing beacon in the dark of the internet, saying 'here I am, I'm on a nice, steady IP address - plenty of time for you to try to hack my computer".
Hacking attempts on personal machines are mercifully very rare, but they do happen. Why tempt fate by leaving your connection running when you don't need it? Disconnect when you go to bed, and reconect in the morning if you work at home. The connection will always be there when you need it.