Mac
All new Macs come with GarageBand recording software. The laptops have a built-in mic, a line-in, or you could hook up a USB or Firewire interface ($100+) with preamps for better sound quality. An interface using Firewire is preferable. Mac laptops start at $1100. Any of them would be more than adequate for what you want to do. I prefer to use Macs. You can be up and running in 20 minutes after you open the box.
Windows
There's a slew of choices and you can do what you want on the $500 weekly special at Best Buy, but you will have to work through issues such as:
Q. What software will I use?
A. Most people here will suggest Reaper. It's good and cheap. You have many other options as well. (Cubase, Pro Tools, Sonar, Adobe Audition, etc)
Q. Will that software run on Windows Vista?
A. Depends. Try and get Windows XP for audio work. You can configure Dell computers with Windows XP still.
Q. Is my Firewire chipset good for using a Firewire interface?
A. This will probably be the hardest thing to figure out...but the answer tends to be no
etc etc etc....do tons of research. Using a Windows-based system can save you money if you find the right solution for you.