I tried MANY laptops and all on a budget simply won't work in my opinion. You need a good middle of the road computer at best to make PT work. I have gone through several desktops before I finally got to where I am now on the road to smooth sailing. Check my specs, but I am using a desktop.
I think the laptops on here that work best are Mac's. If budget didn't kill me I would be using mine on a mac as well. It's just better suited I think. Stay away from all computer that are less than 3 years old. My 2003 did not work well with PT 8!
Just my experience.
I would build a computer to be honest. Much cheaper and you can get on it what PT requires.
That's how I got started on here.
Best of luck