A 5400RPM hard drive is fine especially when considering the price.
The Lenovo has the weakest AMD APU. It is the previous generation Llano APU which has a weaker graphics core. Not sure about the general increase in CPU core performance in the newer Trinity APU. It has the lowest resolution of the three laptops which isn't necessarily a bad thing because of the weak graphics core (iGPU). It is smaller and lighter so it should be easier to carry around. It is also the cheapest. You can expect very modest gaming. It also has some cosmetic damage since it is listed as "Scratch & Dent".
The HP - Pavilion 17.3" Laptop is the next cheapest. It has the newer AMD Trinity APU and thus, has a more powerful iGPU than the Lenovo. The CPU core is also likely to be faster than the Llano; it is listed as 2.7GHz. It has a 1600x900 resolution screen which is higher resolution than the Lenovo. That's good and bad. The higher resolution allows you to see more thing on the desktop at once, but it also means when playing games the iGPU needs to push more pixels which means performance will lag. The fix would be to play games at a lower resolution; like 1366x768. It is a larger 17.3" laptop which means it is heavier. While it only has 4GB of RAM vs. 6GB in the Lenovo, that will not really affect performance.
The 17.3" HP ENVY dv7-7230us is the most expensive and has the most powerful iGPU of the bunch and the CPU core can go up to 2.8GHz. It has 6GB of RAM and a 1600x900 resolution screen. While this laptop will perform the best in games (I think you should play at 1366x768 resolution though) it also does cost a lot more than the other two laptops.
The 17.3" HP ENVY dv7-7230us cost 70% more than the 17.3" HP - Pavilion. Does that mean it will give you 70% better performance? No. I would guess that the integrated Radeon HD 7640G in the Envy will provide about 15% - 20% better performance than the Radeon HD 7520G in the Pavilion. Is it worth spending 70% more money for a 15% - 20% gaming performance improvement? That is your call.
I recommend you look into the following laptops...
15.6" Acer Aspire V3-571G-6407 for $550. It comes equipped with a Core i5-3210m 25.GHz CPU and the nVidia GT 630m. It's more powerful than any of the three you listed. However, the resolution is only 1366x768, but you should get pretty good performance at that resolution with the GT 630m.
15.6" TOSHIBA Satellite S855-S5380 for $650. This one is actually $20 more expensive than the Envy. But it has the dedicated Radeon HD 7680M graphics chip and is more powerful than the nVidia GT 630. It has the same Core i5 CPU as the above laptop and the screen resolution is also 1366x768.