Eeesh. That budget is a little on the low side even for a desktop. And Laptops usually carry a bit of a price premium. You might want to add those two numbers together as your starting point.
As well as what Hunt said,
Some ideas for a Laptop Video Editing PC
-NOTE only 1 hard drive in above, so you will need to add a 2nd drive or use eSata for video files
-or Google "ASUS G74SX-BBK7" (without the quote "" marks)
-or another brand laptop with the following features
-the newer sandy bridge 2720 or 2820 quad processor
-and nvidia graphics preferably the 460m, 485m is a bit much
-1280x900 display with OpenGL 2.0-compatible graphics card
-and 8 or 16 gig ram and Win7 64bit Pro
-and 2 internal 7200 HDDs minimum
Thanks for the answers, my friends says that a laptop with Intel i3 - i5, 4 gb ram is good enough. He is an electro engineer and says that he uses programs that are more demandig with i3 and that i7 would be overkill.
BFTB (Bang-for-the-buck) wise, this is about the best you can get for a decent price: http://www.takeitnow.nl/product/6525583/?c_id=2661. If you go for lower specs, you can forget about:
to work while I travel
because it will be too slow to get any work done.
Your friend does not know what he is talking about and probably does not even realize that PR is very good in threading in contrast to his own programs. Even an i5 laptop is at least more than 7 times slower than a fast system, despite having 8 GB RAM, a good nVidia CUDA enabled card and a SSD plus a 7200 disk. An i3 is intolerably slow, at least by a factor 15 slower if the rest of the system is up to par, but with your budget and 4 GB memory, all you will get is a laptop that is at least 40 times slower than a desktop. Just wondering how many hours of travel you intend to spend to get anything done in those hours.
>my friends says
And this is based on HOW much experience with Premiere Pro?
As Harm noted, a $500 to $800 laptop cannot run Premiere Pro at all (at least not to anywhere near your satisfaction): Generally speaking, such a laptop performs much slower than even a $300 desktop.