Help me choose 500$ budged laptop

I know this is a really low budged but for my country it's what I can afford, so... Firstly, I still have not decided if I will be purchasing a laptop with integraded card only or + dedicated graphics card(Becaus I wana ask you will the laptop with integraded card last longer than with the dedicated).
I know some pros and cons of the integraded only or with dedicated:
pros:
1)Integraded only = less heat, more energy efficient, more battery time, more ?lifespan?(still not sure if it's true)
2)dedicated = better performance, more reliable
cons:
Cons are the exact oposite of the pros
1)Integraded only = not good performace , not reliable
2)dedicated = more heat, more energy inefficient, less better time, less ?lifespan?(still not sure if it's true)

So moving to the next question about the laptops
Here are some that I have found in my country

/1/ Starting with the once incase i will go with integraded graphics(only 1 that is best for price/quality i've found):
1)asus -
Intel Core i5-5200U / 2.20 GHz;
RAM 4GB;
Intel HD Graphics 5500;
15.6'' 1920x1080, FHD LED non-glare type;
1 TB 5400 rpm HDD
38WHrs, Li-ion Polymer Battery Pack, 5hrs battery life, QuickCharge

/2/ Now the once incase i go with the dedicated:
2)asus -
Core i5-4210U 1.70 GHz;
15.6'' (39.62 cm) 1366x768, Glare;
RAM 6144MB (4GB+2GB);
1 TB 5400 rpm HDD;
NVIDIA GeForce GT 840 2048MB DDR3;
37WHrs, 2S1P, 2-cell Li-ion Polymer Battery Pack

3)acer travelmate -
Intel Core i5-4210U / 1.70 GHz;
15.6" Full HD (1920 x 1080) Matte LED-backlit TFT LCD;
4096MB DDR3;
1 TB 5400 rpm HDD;
NVIDIA® GeForce® 840M 2GB;
6 Cell Battery pack

4)acer aspire e5-572g -
Intel Core i5-4210M 2.60 GHz;
15.6" (39.62 cm) 1366x768, LED-backlit CineCrystal;
8192MB DDR3L;
1 TB 5400 rpm HDD;
nVidia GeForce 840M 2048MB DDR3;
56 Wh 5000 mAh 11.1 V 6-cell Li-ion battery pack, up to 6 hours (based on MobileMark 2012 test results)

5)asus -
Intel Core i5-4200H / 2.80 GHz
4096MB 1600MHz
1 TB 5400 rpm HDD
15.6' hd (1366x76 led anti-glare
NVIDIA Geforce GTX850 2048MB DDR3
44WHrs, 4S1P, 4 cell Li-ion Battery Pack

So this are the models that I can afford starting from the cheapest( although they all are little over the budged).

******In addition I forgot to say for what I will be using the laptop. Mostly it will be for movies, internet, music, and light gaming like: Terraria, Minecraft, Starbound, Trine, Hearstone not more than that.
I am looking in laptop:
-battery time wich is important;
-the built quality(not so good at this price but still);
-the life of the laptop
-the screen is VERY important for me!

Well i will be glad if you can help me with the choise and the questions!