770.23 USD is actually plentiful for a decent gaming rig. Here's a basic build suggestion. Add and subtract as you need (I know shipping for Finland can cannibalize some of the costs).
https://pcpartpicker.com/list/Lz4fBP
I didn't include the cost of Windows 10 because it's going to take a chunk out of the hardware costs (nearly 80 dollars if you buy Windows 8.1 pro and do the free upgrade to 10, or 120+ USD for Windows 10 pro). For now, you can run Ubuntu Linux and still play many games like Shadow of Mordor, Alien : Isolation, and Rocket League.
If you already have a previous build that has Windows on it, you can still install that OS onto the new computer, assuming you kept the disc and license code.