The Pentium G3258 is strong enough for most games. The GT610 is hopeless, it is not a gaming card.
Your first move should be video. Use this table of video performance (http://www.tomshardware.com/reviews/gpu-hierarchy,4388.html) then consider how much you really want to spend. A $150 video card will be a huge improvement, like this one:
http://www.tomshardware.com/reviews/asus-geforce-gtx-950-strix,4270.html But if you want to spend the money for the gtx 970 go for it. It'll be great. Note if you budget is only $100 you can still get a video card that will be hugely better than the gt 610 you have.
Second move should be to OC the pentium G3258 up to 4 ghz or so. Your MB supports this and almost all the G3258 chips will hit 4ghz at low, relatively safe voltage like 1.2 volts.
If you want still more gaming performance than the G3258 offers, I think the i5-4690 is the best price/performer that fits your board. The additional strength of the i7 CPUs typically does not help gaming.