Hello everyone. What is the best operating system for this PC : Sapphire Radeon HD7770 1GB DDR5 128-bit, 8 GB RAM, Processor AMD FX-6300 3.5 Ghz,HDD 500 GB ? (W7 or W8)

Regardless of your system, for me Win7 is always better than Win8.

Could you please tell me why ?

IMHO Win 7 interface is way more intuitive and practical and the retrocompatibility should be better, we are speaking of Good Old Games after all.

I went from Win 7 to win 10 and i'm missing my old OS.

Anyway you can search on the net and make your own opinion :)

The system specs are fine with both Windows versions. Also both OSs are equally stable.
So your decision should be made based on some features.

Windows 7 OS is more compatible with older software than 8 (you mean 8.1, I guess). Its start menu and UI logic are oriented to keyboard and mouse controls, while 8 OS is designed with a touch screen or stylus in mind.

On the other hand on Windows 8 you can use Metro applications and you can have more options if you're a .NET developer (like programming desktop applications in javascript).

So, in my opinion if you have a touch screen or you're a .NET developer or you need/like Metro mobile like applications go for 8, otherwise 7 will be a better choice as long as Microsoft keeps supporting 7 of course.

EDIT: Whichever your choice, remember to turn off automatic updates and select and apply them manually when a notification will appear, else the system will eventually be "upgraded" to Windows 10.

Popular prejudice, mostly.

You have more than 4gb of RAM so you would need a 64bit OS to get the best out of the system. As for which version you should take, well that's very subjective. There are those who mock anyone not sucking the latest release patch out of M$ teat as its developed, and they will of course tell you Win 10. There are those who will stand by Win 7 to the end. Me, am half hearted about any of it, had Win7 for ages and its good, but now am stuck with 8.1 currently. I don't like the way Win10 has been released, or the things it may/may not be doing behind the scenes, so I am not jumping to it yet, however saying that you could try it for a month if you have 7 or 8 as its a free upgrade which you can downgrade within a month if you don't like it. Simple answer, try them out and see what you like, remember unless you are only looking to mash your hands across the screen, get classicshell to get start menu and proper PC control back, fecking metro interface should be banned on the basis of user abuse.