The short answer, according to our resident notebook guru, Justin Jaffe, is that most notebooks ship with one of three drive options: a DVD-ROM drive, a CD-RW/DVD-ROM combo, or a multiformat DVD burner. Since you specifically want one that can read and write DVDs, chances are you'll find a laptop that already has a multiformat burner, which means the -R/RW and +R/RW issue is pretty much irrelevant to you; you can use either the plus or dash media. And yes, all DVD burners read and burn both DVDs and CDs.
The long answer requires delving into the history of the DVD formats. Once upon a time, in 1997, Pioneer released the first DVD-R drive. DVD-RW followed in 2001. The -R/RW format is supported by members of the DVD Forum. The DVD+RW format appeared in late 2001, supported by the DVD+RW Alliance, and the DVD+R format was released in mid-2002. Though the media and drives for the plus and dash formats look the same superficially, there are some technological differences. Both camps will argue the superiority of their formats until they're blue in the face, but from the perspective of the standard consumer, the plus and dash formats are basically equal. (Many people draw similarities between this and the VHS/Betamax war, but so far, there's no clear-cut winner.) Just remember, if you have a -R/RW burner, you'll need to use -R/RW media. The same goes for +R/RW burners and media.
Luckily, many companies are members of both forums and, as such, have released a deluge of multiformat drives into the market. So for most people who are just now setting out to buy a DVD drive, a multiformat is the way to go. You'll be able to burn and read DVD-R/RW, DVD+R/RW, and CD-R/RW.