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Don't get too worried about all the specifics... or even the brand, for that matter, as long as it's one of the "big" names... HP being just one (Toshiba, Dell, Compaq, Gateway, ACER, being some others).
You need a dual core processor that's at least 2GHz in speed.
You need 4GB of RAM.
You need a 250GB to 320GB hard drive.
You need a good video card with at least 128MB of its own RAM (preferably 256, though in a notebook, that can get expensive).
You need a good audio card... specifics, when it comes to notebooks, pretty much don't matter. They're all more or less the same.
You need a good, very bright, very crisp/sharp LCD monitor that's no smaller than 15.4-inches, and has a resolution of at least 1280x800.
You need a modem (not a cable or DSL modem, but an old fashioned 56Kbps telephone modem... even if it's only a "soft" modem).
You need both wired and wireless Ethernet connectivity.
You probably (but not necessarily need) Bluetooth.
Your CD/DVD drive needs to be able to both read and BURN (write) CDs and DVDs. If it's also capable of HD, LighScribe and/or BluRay, all the better, but those things are just extras.
It's nice if a camera is built-in (1.3 megapixels is fine; 2.0 megapixels is better), and stereo microphones (both of these things usually in the top rail of the cover, above the LCD monitor).
Most notebooks have speakers in them, so don't worry about that.
If you can afford to get a memory card reader built-in (4-in-1 or greater), that would be very good, too.
And most notebooks with all of these things will also have all the right input/output ports and slots and other such things; and a keyboard and touchpad... so those are things you don't have to sweat too much.
Microsoft Windows Vista Home Premium is perfect. If there's a free upgrade to Windows 7 when it's finally released, all the better (but, if not, Vista's fine).
Beyond all that, honestly, you're probably wasting a lot of time worrying about. If you knew what I knew about where all the manufacturers get their parts, and how everything is made, then you'd realize that brand matters little other than that the better and bigger the brand, the more easily and quickly you can get it fixed.
Beyond that, you may want to get an extra AC adapter so you can have one at home, always plugged-in to the wall outlet (so you don't always have to bend down behind the desk), and another in your bag so you'll have AC power when you're out and about.
You may also, if you work, when you're out and about, in dark places where it's hard to see the keyboard (because the light from the LCD monitor is nearly never enough), then you may want to spend a few bucks on one of those little keyboard light thingies that plugs-in to a USB port, and has a little flexible gooseneck that lets you point the little white LED light down at the keyboard.
You'll want a carrying case, of course.
Beyond that, worry not.
Just pick the biggest name with all that I have said, which costs the least.
Also, don't be afraid to save money and buy a refurbished notebook. Just make sure that you're buying from a reputable store; and that the notebook was FACTORY refurbed, with a full warranty.
Hope that helps.