Will the following setup work really good for gaming?

first off, i wouldn't recommend the cpu you're using unless you're on a tight budget.
then, the radeon HD 6670 is older, get one of the 7000 series for about the same price.
also, for gaming you will need 8 gb ram, 4 is not enough in most games.
the rest should be fine.

you could possibly go for the amd FX 6350, for about 25 euro's more, you keep the same socket, and you will get more performance out of your pc.

No.

First, logisys power supplies are dangerous. If they fail, they can damage anything they are connected to.
They are tier 5 units(NOT RECOMMENDED. Replace ASAP on this list:
https://community.newegg.com/eggxpert/computer_hardware/f/135081/t/45344.aspx?Redirected=true

The rest of your parts are workable, but not really very good, and will have a problem upgrading.
Why:

Few games use more than 2-3 cores, upgrading to a FX-63-- or 8350 will add cores but are not that much faster.

a 4gb kit will likely need to be replaced to add ram since you only have two ram slots.

6670 is older tech and is not much faster than integrated graphics of today. With a 450w psu that may not deliver 450w, your graphics card upgrades will be limited.

USB wifi dongles tend to be weak. You might be better off with a add in pci/pcie card.

A cheap budget rig might be doable with an A10 apu, but your upgrades are even more restrictive.

I like planning for the future if it does not cost too much.
Here is a post I made for that consideration.
It might exceed your budget, but if you do not get what you need your budget is wasted.


------------------------------ budget build ---------------------------
For a budget build, I like to recommend that one builds for future expandability.
That means paying a bit more up front for some parts that allow for an easier future upgrade.
Let me start where you might not expect:
1. Buy a good 620w psu. Such a unit will run any future graphics card.
I would normally suggest Seasonic 620w:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
But this EVGA 600w unit is going for a very good price:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
2. Buy a Z97 based motherboard. Z97 will allow you to install a overclockable cpu and even offer a future 14nm broadwell upgrade.
You should fine one for about $100.
Here is a M-ATX : http://www.newegg.com/Product/Product.aspx?Item=N82E168...
3. I suggest a G3258. It is a overclockable dual core at a budget price of about $75.
Here is what it can do: http://techreport.com/review/26735/overclocking-intel-p...
In time, you can upgrade to any cpu that you want and market the G3258.
4. The intel stock cooler will do the job up to a point. But, I suggest a $30 tower type cooler like the cm hyper212 with a 120mm fan. It will cool better and be quieter under load.
5. For ram, speed is not important. Buy a 8gb kit of 2 x 4gb DDR3 1.5v ram.
6. Cases are a personal thing. Buy one you love. Most will do the job for <$50.
It would be hard to beat $34 delivered for this Antec GX500 :
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
7. The graphics card is the most important component for gaming. My usual rule of thumb is to budget 2x the cpu cost for the graphics card. I like the GTX750ti and EVGA as a brand.
Here is a superclock version:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
You could go stronger in the video card if your budget permits and your games need it.
On the other hand, you could build using the integrated graphics and see how you do.
By deferring on the graphics card, you will get a better idea of what you really need.
Integrated is fine for sims, but not fast action games.
8. Lastly, I will never build again without a SSD for the "C" drive. It makes everything you do so much quicker. 120gb will hold the OS and a handful of games. With 240gb you may never need a hard drive at all. Defer on a hard drive until your ssd approaches 90% full.

-------------good luck------------