KDE wasn't unfinished in the sense for what it was released. It was a platform release, not a user release. The distributions in this case made the mistake ;-).

Anyway, a thread like this should not exist. There is no "Gnome" vs "KDE", there is only the user, with the freedom to choose. Both projects inspire each other with features and new approaches. KDE and Gnome are both valid choices, depending on the users needs.

I'll write two parts. The first is short, so I'll start out with it. Consider buying another just another wireless card (as an Intel Wireless card, or one with an atheros chipset) to replace the Broadcom in your Laptop. This will probably be the cheapest solution, and should work.

As you wrote you're not an expert, I won't hassle you with technical details about why not to buy broadcom devices, but I can ensure you, that broadcom does a great job making the kernel developers life harder than it must and should be.

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Secondly, if you're really thinking about a new laptop. I can suggest Dell Latitude (I personally call a latitude e5500 my own, and i'm really happy with that piece, my girlfriend uses a Dell Vostro 1500 on Ubuntu, which worked great out of the box as well). It runs all hardware out of the box, means no hassles, no configuring at all.
Probably some people will disagree with the vendor (Dell), but I'm perfectly satisfied.

If you buy a laptop, make two things sure:
Get a video card which has a good support, which nowdays means NVidia (i don't like them, and don't have one, but they're currently the best ones).
A valid choice for cards which work is Intel (4500 HD in example). I have a 4500 HD, but I want to say a few words of warning: It's not fast, not thought for a lot of 3D and the drivers arn't that good at the moment, but they do the job. If I was just a user, I'd pick NVidida (for sure). But it's perfectly fine for systems which you'd like to work with, where you don't need a lot of 3D (and it's the cheaper choice).
No ATI graphics card if you want to make your life easier!

For your wireless device, you should pick either Intel or a card with an atheros chipset (as my former speaker already mentioned). That's the way to go in Linux at the moment, if you want stable and good drivers.