are usually mutually exclusive, but as it happens...............
My eldest daughter has a company laptop but her company locks it down so she can't use it for personal email/web-surfing etc.
They provide her with a broadband connection at home though, so she asked me to find her exactly what you're looking for - a cheap laptop that she could just use for the web, and for email. We got her a second-hand machine from this company
Her Toshiba came with a warranty, and she's delighted with it.