What laptop can you suggest?

If we're talking video editing, laptops are the wrong way to go. Laptops are about the worst platform you can come up with for video editing. Small screen, lower power components, and of course the heat generated from the video editing will cause premature failure of the unit. Plus at $700 or less, you probably aren't going to find anything that meets your specs to begin with.

Now if we were talking desktops, and not all-in-ones, it'd be a whole other story. Dell's XPS desktop line would probably about have you covered and in the price range you're looking at if you already have a monitor. Or you could build your own... Might cost a little more, but if you take your time and pick your components well, you have near infinite flexibility for upgrades.

Not sure there's any other major brand I could recommend for desktops. Lenovo's warranty commitment is questionable given how they release a new model every 6-8 months. ASUS, I would call an extremely racist company, to the point where they go out of their way to racially discriminate against employees, plus their repair program isn't something you want to deal with because it involves you paying to ship the computer to their subcontractor in Milpitas, CA where it will sit for 2-4 weeks waiting for some part to make its way over on a cargo freighter from China and then they'll probably botch the repair anyway. I had a friend whose job with ASUS was to deal with customers like that, until he complained about his Asian coworkers harassing him because he's white. ASUS refuses to investigate his claims of being harassed and discriminated against, despite the HR department clearly recognizing that they were made, but will go as far as to get someone to file a false police report against him. HP is not really showing any signs that Meg Whitman will be able to turn around the PC business quality wise and if you do a quick search you can find R. Profitt's numerous tellings of how HP walked out on a warranty on a unit he bought. iBuyPower and CyberPowerPC are little more than scam artists posing as PC builders if you read a lot of online reviews. Then there's Apple where either you get the low end Mac Mini, which has all of the drawbacks of a laptop and none of the benefits of a desktop, or the high end Mac Pro which is well outside your price range.

The TLDR version: Get a desktop for video editing, either Dell or build your own.