Computer for League of Legends

League of legends is very light game. There are no big demand neither for CPU neither for GPU. So if you wonder what computer you need to play it. Don't be scared it will run on almost any PC. A few word about its requirements. The recommendations are"GeForce 8800 or equivalent video card (Dedicated GPU with 512MB+ Video Memory(VRAM))" or "GT330M" for laptop and these are old outdated GPUs. Even GPU like GT610 can run LoL on lower settings. And higher priced video card like HD7770, GT650 and video card from next tier like HD7870 or GT660(or 760 since NVIDIA released 7th series) are just overkill.

The ranking is like this:

GT610/HD6450 low settings
GT630/HD6670 enough for max settings
GT650/Radeon HD7770 max settings very high frame rate(over 60)
GT660/Radeon HD7870 overkill

What about the integrated graphics?

intel HD4000 - you can play at lower settings at full HD
A8-5600K - same as HD 4000
A10-5800K -if you have fast ram it can even reach the level of Radeon HD6670 DDR3.

For CPU there are no problems at all. Pretty much any dual or more core CPU will do the job. But nowadays there are cheap quad core CPUs available so here is one suggestion for computer for League of Legends with Quad core AMD processor and video card enough to play at frame rates around 100 fps.

ASROCK FM2A75 PRO4-M AMD A75 FM2
ATHLON X4 750K /BOX/FM2
CORSAIR 1x4GB VALUE SELECT DDR3 1600Mhz 1.5V
500GB SEAGATE 7200/6GB/16MB
SAPPHIRE HD7750 1G GD5
CM K350 W/600W PSU

Entry Level budget gaming computer

Here  there are two suggestions for budget gaming computer.

AMD:
CPU - AMD FX-4300
Motherboard - ASROCK 970 PRO3 /AMD970/AM3+
RAM - any 2x4 GB running at 1600 MHz
Hard drive - Seagate Barracuda ST1000DM003 1TB
Case - COOLER MASTER Elite 350 with 500W powersuply
Video card - Radeon HD7790 or GTX 650 Ti boost

Intel:
CPU - Intel i3-3220
Motherboard - ASROCK B75M-GL
RAM - any 2x4 GB running at 1600 MHz
Hard drive - Seagate Barracuda ST1000DM003 1TB
Case - COOLER MASTER Elite 350 with 500W powersuply
Video card  - Radeon HD7790 or GTX 650 Ti boost

So lets see the CPUs  FX-4300 vs i3-3220 both are similar priced with similar performance. FX-4300 is quad core and i3-3220 is dual core featuring Hyper Thread technology making this dual core processor working almost like quad core.
The main difference between those is the single core performance. Intel i3-3220 has better single core performance and this mean that every program and game that is not optimized for work on multi-core processors will work faster on the i3. FX-4300 has better multi-core performance making it better for games and programs which are able to utilize all of its  four cores.
The latest games like Far Cry 3, Battlefield 3, use more cores so they have better performance on FX-4300.   The older games however have better performance on i3-3220 and here are all those catching games which keep you on the PC with hours like World of Warcraft, Diablo 3, Starcraft 2, League of Legends, Dota 2 HoN and so on. The difference between these two processors however is not so big so i place them evenly its just a personal choice if you are fan of AMD or Intel go for it. If not just pick one!

The both motherboards are similar priced and actually for gaming PC they have more than enough. Both have USB 3.0.

Memory 2x4GB RAM running at 1600 MHz is enough for this computer. Even too much, to save some cash its possible to get only 4 GB. The brand of the memory and the the memory timings are not so important just pick one for example A-data which offer good price/performance memory modules. Even memory at 1333 MHz will do the job but lets not be too cheap since the difference is only few bucks.

In this gaming configuration we are saving from the computer case. So there will be more money available for the video card. This case offer enough for this configuration, there is good enough airflow to keep the components cool there is one rear fan included with the case, the 500 W power supply is more that enough for this configuration. There is one flaw however the front panel doesn't support USB 3.0 and this mean that if  you want to you the USB 3.0 you have to use the rear ports.

The hard drive is again 1TB Seagate Barracuda with good price, there is not so much to be said about it either.

Last thing is the video card. After comparing FX-4300 vs i3-3220 its time to compare the video cards.
Radeon HD7790 vs GTX 650 Ti boost. Again the performance of the both cards are similar, the choice must come from the games which will be played.
Here is one comparision between the both cards Radeon HD 7790 1GB & NVIDIA GeForce GTX 650 Ti BOOST 2GB Review. You can see that there is no clear advantage. In some games the GTX 650 is better in other HD7790. If you will play games that use for example NVIDIA PHYSX then go for GTX-650.

Best everyday pc

If You wonder what is the best PC for everyday use without spending too much money. Here is the answer.

CPU - AMD A10-5800K
Motherboard - ASRock FM2A75 Pro4
RAM - Kingston HyperX Black Series 8GB (2 x 4GB) DDR3 1600
Hard drive - Seagate Barracuda ST1000DM003 1TB
SSD - Intel 335 Series Jay Crest SSDSC2CT180A4K5 2.5" 180GB
case - COOLER MASTER Storm Enforcer
psu - COOLER MASTER eXtreme Power Plus RS500-PCARD3-US 500W

First lets start with the CPU. One good all in one CPU is the AMD A10-5800K. This is a quad core CPU able to do all everyday tasks like browsing and watching movies and games. The integrated in the CPU Radeon HD 7660D graphics are capable of doing more than watching movies. I'ts a surprisingly powerfull for integrated graphic card. It's capable of playing games like Crysis 2 at full hd ressolution. Games like LOL, Dota 2, HoN and WoW are just peace of cake for it. And even the latest 3d shooters at low settings.

Second the motherboard: ASRock FM2A75 Pro4 one very good motherboards offering sata3 conection up to 6.0GB.s and USB 3.0 ports. There are better motherboiard offering additional featers but most of us actually will never us them.

For every day PC there is not need of huge amount of RAM 8GB is completely enough (even more than enough) a good RAM is Kingston HyperX Black Series 8GB (2 x 4GB) DDR3 1600. This is 2x4GB kit intended to work in dual channel which is good for the integrated graphics. So even if you like some other manufacturer more or want to put more RAM use 2 blocks of RAM not 1, because you need the dual channel for the better graphics.

Hard drive, Seagate Barracuda ST1000DM003 1TB one good hard drive for the price, I have a western digital caviar black hard drive which is little bit faster but a little bit noisier so i recommend this one because its more quiet.

SSD drive. Now this is where the money saved from the CPU, GPU and motherboard will go. This is one of the fastest SSD ever - Intel 335 Series Jay Crest SSDSC2CT180A4K5 2.5" 180GB. Why 180GB? Because there is enough place for operation system , for all browsers , games, and whatever programs you are using. Yes this is 180GB ssd for price arround 170-180$ you pay 1$ per GB and actually less dollar per 1GB compared to solid state drives with less capacity. And why to pay for it? The answer is one "pure pleasure". The computer is loading really fast. When you want to open a browser or anything everything happens in the same moment. You click on the browser and the browser opens right away click on program and there it is for insignificant loading time. So this is must have and changes the way that your computer works. Everything is going faster!

Now lets choose one pc case COOLER MASTER Storm Enforcer is actually a gaming case but it has all that we need at good price. It has 4 USB ports on the top edge of the case, place where they are easy to use 2 of this ports are blue colored and they are usb 3.0 and they can be connected to the usb3.0 header on the motherboard. The case has nice airflow and it will keep all the components inside pretty cold. If this case doesn't look so good to you, or doesn't fit your style you can always change it with other one.
One good power supply is COOLER MASTER eXtreme Power Plus RS500-PCARD3-US 500W power supply. 500W is more that what we need but this power supply is coming at good price and it has pretty high efficiency.