Ok EVGA built Motherboards back in 2009 and Gpu. I was conceived in 1944 So being retired and can't seems to gather enough money on retirement to build a new computer. and this one is working Great after all these years. Here is what I have.
1. EVGA 122-YW-E173 Motherboard 750 SLI
2. Intel QX6850 Extreme  Socket LGA 775
3. 4X2gig DDR2 1333fsb 800 Mkz  4-4-4-12
4. EVGA 550TI Gpu             
5. Thermotake TR2RX 850 W Power Supply          
6. LG 40" 1080X1620 Tv for monitor       
    
Ok here is what I am wondering. I am wanting some new games. FAR CRY and CRYSIS are about worn out. I wonder IF a 1060 GPu  will power most new shooter games and possibly going to 4X on the TV Later. If not what other changes could I try? Nothing is overclocked and the Cpu is Liquid Cooled because of the 130 watt.

A 1060 should work in your system. You will most likely bottleneck that GPU but it will still be quite an upgrade. What is the actual resolution you game at? The 1080x1620 looks like a typo. The higher the resolution the lower your bottleneck. Going to 1440p may help but honestly, that architecture is so old you still may bottleneck.
 
Add more RAM. Quick and easy upgrade. Try to go to 8gb of the fastest stuff you can find. May be tricky since it's an old system.
 
Next I would overclock your CPU. I used to have a QX6850 back in the day. It's a good chip but a disappointing overclocker. With that said, you should be able to hit 3.6ghz easy and stable. I had mine on a 780i FTW under a Megahalem at 3.6ghz. You're under water so you shouldn't trouble cooling it.
 
But really, I would grab a Q9650 off ebay for around $100. Those chips hit 4-4.2ghz easy. 
 
Your last option and honestly the route I would go is to pick up some used parts in the marketplace here. I've seen some X99 mobos going for around $150. Pick up a used i7 and some RAM and you're off to races. The X Intel chipsets tend to last quite some time. I'm still running my X58 system with a current GPU and keeping up with the best of them. Spending a bit more now will allow you to pinch pennies later.