Help on details of Laptop Manufacturer and Graphics Manufacturer?

Ok, recently i've been thinking of buying a new laptop and i searched on the internet… But what I can't do is decide on some facetors such as the laptop manufacturer and graphics manufacturer and which ones are best. My budget is medium range… Neither too low nor too high… As I'm gonna buy it from Bangladesh my range is around Tk. 50,000 (U$D 650).many brands are available here.here are my questions below

1. Which Laptop manufacturer is better between Lenovo, Dell, HP, Acer and Asus?

2. Which integrated graphics are better between Intel, Nvidia, ATI and AMD?

I will use the laptop for casual gaming and stuff

For that price range, Lenovo and HP are good. Nvidia is the best integrated graphics but you won't find anything in that price range, and AMD is the second best integrated graphics.

First determine the graphics.
Intel CPU has Intel integrated unless there's an added card
A Series AMD has a co-packaged graphics IC, and may also have a separate card as usually AMD
The separate card can be NVidia or AMD. AMD bought ATI many years ago. There's no ATI graphics any more.
Intel graphics can google the CPU to get to the Intel page.
ARK | Intel® Core…
http://ark.intel.com/...e-2_40-GHz
i3-4000M has Intel® HD Graphics 4600
The A series in latest level is tricky.
A8-6410 for example if no added card has Radeon R5. That is R5 6410 graphics
A10-5750M has HD 8650G
So, you must determine the graphics processor.
Separate cards work when plugged into AC power only.
compare graphics
This web site shows GPU compare
http://www.game-debate.com/...600-mobile
You start typing the GPU and a pull-down of choices lets you select if you get it correctly.
R5 6410 is 17% BELOW HD 4600
GT 840M is 55% above HD 4600
http://www.game-debate.com/...600-mobile
840M is 34% above hd 8650G
http://www.game-debate.com/...n-hd-8650g
This very slow load high data site is GPU to gaming
http://www.notebookcheck.net/...849.0.html
The AMD A series graphics are not shown unless titled like 8650G

Graphics processor is the most important item in gaming.

Look up CPU scores here for general speed
http://www.cpubenchmark.net/...u_list.php
A fast CPU does not help a slow graphics processor. A slow CPU will be noticed outside of gaming.
If CPU scores are within 10% or so, it is not important.

That should be enough to evaluate gaming. RAM can usually be upgraded to 8GB as the most you need in gaming, but start with at least 4GB and 8 is preferred.

Brands:
Lenovo, Dell, HP, Acer, Asus, MSI, Toshiba

Acer is always at the bottom. They will use the cheapest parts that meet the specifications shown.
Spongy keys, washed out screens, fast fail of the DC input jack, overheating, etc are most common to Acer, but, they are often the highest performance for the money, so see what you give up for quality. You may want to take your chances with an Acer.

Next level - consumer grade:
Lenovo Essentials G series, HP Pavilion, Dell Inspiron, Toshiba Satellite, and cheap Asus all go here.
The cheap Asus and Lenovo Essentials MAY be slightly better, but just look for reviews among these.
They are very similar as just a little better than Acer. Cheap Asus is a judgement. If the specifications match the other brands here at the same price, be assured it is a "cheap Asus". MSI does not offer cheap laptops.

Better:
Lenovo Ideapad Y, Z, U, Yoga, Flex
HP Envy and Pro., Dell XPS,
Toshiba Qosmio, Portege, Tecra
Asus and MSI entertainment level

Top - Lenovo Thinkpad, Apple, Asus and MSI gaming level with 1080p displays and top level graphics gpus

Might find a leftover Samsung. They are very good but exitting the standard laptop business.

Note that NVIDIA GT 820M is not a strong graphics and may be found in your price.
24% over hd 4400
http://www.game-debate.com/...400-mobile
13% over hd 4600.
R6 7300 of A10-7300 is slightly better than Nvidia gt 820M

It takes time to shop carefully.