I would like to find an all around good laptop in the 550-700 dollar range. I will probably be playing only things like CS:GO and League of Legends sometimes, other than that its for schoolwork. Anything is helpful!
Those game are not very demanding especially LoL. Integrated graphics like the Intel HD 620 found in 7th generation Intel Core series CPUs will have no problems playing those games. Though to get 50+ FPS in CSGO at 1080p resolution most of the time you would need to use low graphic settings.
Having said that, the most powerful laptop you can buy for less than $700 USD is the following Lenovo Ideapad 700 with a quad core i5-6300HQ and nVidia GTX 950m. Though from what recall battery life is only about 4 to 5 hours with "average" usage (no games). It costs $669.
For a less expensive laptop there is the Lenovo Ideapad 510 which has a dual core i5-6200u and nVidia 940mx for $550. The 940mx is probably around 20% less powerful than the GTX 950mx, but it is certainly more powerful than Intel's integrated graphics. Based on reviews, the laptop only has around a 4 or 4.5 hour battery life based on average usage.
If you want something with very long battery life then there is the ASUS P-Series P2540UA-AB51 for $500 with an i5-7200u and Intel HD 620. A couple of reviews indicates the battery can last up to 8 or 9 hours based on the synthetic testing methods used. You are basically giving up gaming performance for battery life.