Hi There!
Are you buying internationally, or can you tell us your budget and link a few sites where we could see a few options?
That's not a bad laptop really, the 740 while lower end won't have issues playing gamines on low/medium settings
Check in Control Panel -> Sounds and ensure the microphone is detected and set as your default input device, also check your sound mixer to ensure it is not muted.
Run the Windows Microphone setup wizard to get a comfortable recording level.
I bought my girlfriend the same laptop!
It'll have no issues playing LoL and TF2 - TF2 is Source based and LoL is not that demanding either. One thing I'd recomennd is swapping the hard drive for something better, it's a laptop 5,400 drive and they'er slow, get an SSD or a Hybrid drive at least.