There's a solid chance you can meet all your needs with a $450 laptop if you're upgrading from like a 9500GT and Athon x2 5000+. At the $450 price point, the first question you would have to answer is--do you want moderate gaming (AMD) or a particularly powerful processor and only the lightest of gaming (Intel)?
You can have both a powerful CPU and quality gaming if you go with the $680 Lenovo above--a fine choice.
EDIT: Best Buy seems to have removed both the laptops I linked. So I'll just remove this portion of my response.
As far as manufacturer--I've had bad and good experiences with a lot of brands and I don't particularly dislike or trust anyone. One manufacturer I've never heard bad stuff about is Lenovo...so that is impressive actually. I'm sorry this doesn't specifically apply to the question at your price point. But it does put some tools at your fingertips for comparing components and finding deals yourself.
My vote is for the Lenovo Y570. That's a very solid deal.
I wouldn't worry too much about the screen res. IMO, 1366x768 vs 1920x1080 is real difference, but 1366x768 vs 1600x900 not that much. Also, you get lower performance if you play on higher resolution.
Actually, it depends on what you are doing.
My 14" Lenovo IdeaPad Y470 has a 1366x768 resolution screen. I find that the low resolution affects my ability to multitask with a few open windows / programs on my screen. Even when I attempt to arrange all three windows / programs on the screen I find that not all the information that I need is on the screen all at once. I would need to constantly switch between windows / programs to gather the information I need for whatever task I am trying to do.
However, trying to find a good performing "moderate gaming laptop" with a $700 - $800 budget that has a 1600x900 resolution screen is difficult at best. Not to mention it's a 14" laptop; 15.6" is actually too big physically for my liking.
For productivity, a higher-res screen is a big deal. For gaming, lower-res is better in my opinion because I care much more about gaming at native resolution than any specific high resolution. And 1366x768 is half as many pixels as 1920x1080, which pretty much means double the framerate if your CPU is up to the task (and an i5-2410M is).
Yeah, I generally agree that lower resolution is better for games because it places less of a demand the graphics card which is relatively weak compared desktop graphics card.
However, even a low resolution screen can negatively affect gameplay; at least for me. In 1st person games like Crysis and Fallout 3 I generally tend to snipe at my enemies at long ranges without using a sniping rifle I might add. Fewer pixels on the screen generally means long range sniping using iron sights is a bit challenging.
To get 1600x900 resolution in your budget range you'd need to move up to a 17" laptop and settle for a less powerful graphics card.
Example: Acer Aspire AS7741G 17.3" notebook $650
Core i5 480M(2.66GHz) CPU, 4GB RAM, 640GB HDD, 17.3" 1600x900 LCD w/ AMD Radeon HD 6550M. AMD Radeon HD 6650M
The higher 1600x900 resolution will also mean lower FPS for the extra number of pixels the graphics card has to drive.