The acer has decent specs other than the graphics. Intel Integrated is a no-no if you ever want to do gaming, and pretty much the same goes for high def movies.. Not sure if that'd handle the decoding, unless it's all processor based, in which case you're fine.
You're in the same boat for the MSI.
I headed over to Newegg and took a look at what they've got.. Not sure about the warranties, and I'd be sure to get a decent warranty for something that you'll be putting in and out of your backpack every day, but they've got 7 notebooks under $700 with dedicated graphics, and a few more in there as I put the max price to $750.
Newegg's dealsTo narrow it down a bit more, I'd look more at the Intel processors as AMD has been really lost in the dust, especially on the mobile front. I'm not sure how well the warranties they offer extra work, but it'd be worthwhile to see if you could get an extended warranty through the OEM vs the aftermarket warranty.
Out of all of the ones displayed on the page I'd look at this
Acer Aspire the most. It's the only one that's new that has a decent processor (My mom has the Pentium t4500, and while good enough for normal everyday use, you're not going to be doing anything close to actual gaming with it. At least with an i3 you'd have a bit more of a chance to have fun if you felt like it), though it's right at your price point, and a bit over if you add in shipping.
Again, no matter what you get, I'd look at an extended warranty. Most of these are given a 1 year + 1 year accidental damage warranty (so a total of one protected year), and I'd at least try for two full years.