Whilst Times New Roman can be fine in websites going for a more ornate theme, Arial is easier to read 99% of the time. It also reacts better to different colours and sizes, and, on the whole, looks a lot better. That's just my opinion though. Normally I would use a font such as Verdana or Tahoma, but it all depends on the theme of the website.
Best thing is to try both and see which looks best. Good Luck .
I pick Calibri anytime (if I can); it is rounded, gentle, welcoming... and a pleasure to read. Headings don't shout at you but draw you in.... one of the best features of Word 2007 as far as I am concerned
I'm currently a web designer from Chennai, India. I use verdana for small texts. It is very legible even when used in smaller sizes like 11 px. I use arial when I go with normal texts like 14 or 15 px. But I've a love for Georgia.