The parts inside are very substandard. Not sure why the others in this thread are actually recommending them, especially since even the reviews on Lenovo's actual website for these T-series products are poor. And for god's sake, if you want to play games using ANY computer device,
don't get an integrated graphics card. I cannot stress this enough.
Anyway, since you say that the T-450p is the model which interests you
These specifications
are for people who are not looking to do any kind of gaming on their laptop and if any,
only with simple games. (like Sims 4 in Laptop mode or Mirror's Edge at lowest settings) The BEST possible CPU for this model as shown by Lenovo's customization process is the Intel i7-5600U, dual core 3.2GHz. This particular model of CPU includes an Intel HD 5500 integrated graphics card. You'd be lucky if you could play a 2009 game at medium settings. It's a good CPU by itself though.
I don't like the massive amount of bloatware that Lenovo actually admits right in their specifications to installing on the laptop. Those will only slow down the PC and offer services you will likely not desire. The HDDs they allow you to customize into the laptop are subpar, but at least you have the option of SSDs. (even if the maximum capacity is 512GB)
So since you're interested in the T-450 model that has a (maximum) price of
$680, I assume you're ok with any laptop within that range, yes?
Here's an Asus laptop that is actually lower priced than the Lenovo T-450p you're looking at.
http://www.newegg.com/Product/Product.aspx?Item=N82E16834232753
Most top-of-the-line gaming laptops go for $1000-2000, but this one is very entry-level
and yet is still quite powerful in comparison to the average laptop, such as the Lenovos you are looking at. The only downside is the CPU is the one which is low in power. It has an SSD, though, which is very good for PC speed in general. Load times with this laptop must be nice. It has an HDD and an SSD. That's an optimal setup for gamers since you can have games installed on the SSD and all of your other personal files stored on the HDD.
Should also note, this laptop support AC network types so you can use top-of-the-line routers with it for fast speeds if you want fast internet and online gaming.
The graphics card is three times as more powerful than the Lenovo T-450p's. At least, when pushed through a benchmark.
http://www.videocardbenchmark.net/compare.php?cmp[]=2908&cmp[]=3171
Here's an MSI laptop that's going up the gaming laptop ladder.
http://www.newegg.com/Product/Product.aspx?Item=N82E16834152949
This one is barely stronger than the ASUS and you'd have to pay more than usual. The screen is bigger, the CPU is strong, and it includes 8GB memory. It doesn't have an SSD, however, and it's HDD is a slow 5400RPM. It's also a bit heavy at 5.29lbs. Heavy for a small woman, pretty normal for a guy. It would be annoying to lug around for anyone, though. MSI also tends to include some annoying bloatware because of their "gaming community" garbage or whatever. It's... well, it's pretty looking.
Just throwing ideas around. The laptops you're looking are neat for the common consumer, but for gamers they barely fit the criteria. I just want you to be more open to other brands and laptops since you can find laptops more powerful
easily within your range.