1) 4GB for most games is enough, especially for games you support and at those settings:
http://www.digitaltrends.com/computing/new-testing-suggests-pc-games-dont-need-more-than-4gb-of-ram/
2) Make sure you have 64-bit Windows (preferably Windows 10, which can be upgraded from 32 or 64-bit W7/W8 though 32-bit must be a clean upgrade)
3) GPU as said above is by far the biggest difference. The GT610 isn't even a gaming GPU. (do not get an AMD GPU as their drivers use too much CPU processing power for DX11 games and you don't have a lot of that to spare, thus with a good GPU you're going to add to the CPU bottleneck and get lower performance)
How much difference?
Obviously the CPU matters too, but let's just compare:
GT610 - 48 CUDA cores
GTX680 - 1536 CUDA cores
The overall processing power is roughly proportional, so the GTX680 is 32X more powerful. Frequency of GPU, CPU, and the game itself all factor in so it's not exactly proportional but obviously you can do much, much better.
What would I do?
Depends on budget and power supply, but a GTX750Ti or GTX950 are great choices.
i.e.
$100 after $20 rebate, GTX750Ti:
http://pcpartpicker.com/part/evga-video-card-02gp43753kr
$130 after $30 rebate, GTX950:
http://pcpartpicker.com/part/asus-video-card-gtx950m2gd5
Performance?
https://www.techpowerup.com/reviews/EVGA/GTX_950_SSC/30.html
Crunch the numbers and the GTX950 is about 25X more powerful than the GT610. Again, it won't scale like that and the CPU has a big impact but let's just say, much better.
*A game like Tomb Raider which doesn't require a lot of CPU processing when tweaked will suddenly become quite playable with your CPU and a GTX950.
A suitable 450W would be plenty for your CPU and GTX950 (possibly using the MOLEX->6-pin adapter).
Cheers.