Looking on the unending flow of good exclusive games on 'nextgen' consoles aka PS4/X1 I made a desision to put my PC in a decent form and start playing 3rd party games on it. 
So could anybody tell me what kind of machine will I need to play latest PC games with a comfort?
I will play it on my old Plazma HD-ready TV via HDMI and x360 gamepad, so I don't need it to be 1080р on ultra.
1280x720 with 4xAA and 60 fps on high will be more than enough for me.

My current setup is Intel Core Duo E7500, 4 Gb of Ram and 1 Gb AMD HD6800. 

I feel that I need to up my RAM to 8 Gb and change a videocart to smth Nvidia's. 

Any help/advices will be appreciated!

For a start, gaming at 720p, 4GB Ram is totally fine.

GTX750 Ti would be a decent card for 720 gaming. And wouldn't necessarily require you to get a new PSU to support it.

Regards to CPU I'm not sure. First off, upgrade the video card and then test a few games and see where you are at. But for "only" 720p on a PC, I doubt your too far off the mark already if you upgrade your video card.

pick up a R9 290X. they're super cheap right now.

In fact I'm playing Diablo3 on my PC on highest on 1080p/no AA currently with 50-60 fps. But Metro Last Light was totally unplayable for me, even on low with 640x480.

Which version of Metro were you playing though.  Pretty sure the original releases were absolute system hogs for no apparent reason.  The recent "remastered" versions though give the same result, for a lot less power.

EDIT

I suppose in reality, to get a better understanding of where you want and need to be, you could give an indication of how much your willing to spend also.

I wouldn't call it cheap... Heh, its 480 USD now in Russia, I can buy X1/Ps4 with one or two games on this money! Hell, no!

Don't remember, was trying to play it this Spring, it was the latest Metro game IIRC. 

Yeah, this is the graphics card I was looking on! 120USD with some discount...

Yep.  They are the old versions.  The new releases will play "better".  How much better I'm not sure but they will.

The problem you have as far as I can see it is that with your CPU, your already at the top end of what your motherboard can handle in terms of having a good CPU.  If you were to improve that, then your going to have to spend on a new motherboard also.  So that part, I'd upgrade last if necessary or else it will start to get costly.  There are a couple of CPU upgrades you can do though that would just be a swap (IE  X6800) but the gains would be minimal I would expect.

Really, its the Video Card you need to upgrade first as thats what is going to hold you back more than any other component at 720p

Yup. If i'd want to upgrade a CPU it will be easier to build a new PC for me and I don't fell in the right mood to do it currently.

Thank you for the support, its nice feeling when your thoughts align with others clever thoughts well! )