Be careful with getting a dual core option.
An excerpt from Toms CPU guide.
http://www.tomshardware.com/reviews/gaming-cpu-review-overclock,3106.html
" Unfortunately, Dragon Age Inquisition will not run on a dual-core processor. Performance under Far Cry 4 was also problematic due to apparently poor PC port optimization (at least there’s a fix available for Far Cry). Dual-core CPUs aren’t inherently to blame for this. Still, you could become a victim of lazy development moving forward if companies like BioWare and Ubisoft Montreal aren’t held accountable by PC gamers for sloppy work."
Just be warned that if this is a trend in software developers. Your dual core could suddenly become a paper weight. Okay well not a paper weight, but it would play video nicely.
An option that wont break the bank could be the A10 series from AMD. The prices are dropping fast and for a budget PC with DX12 coming out that will allow the APU to SLI/Crossfire with any card you eventually drop in it. I find it hard to leave them out of the picture.
I will likely get a lot of hate responses for recommending this but you are on a budget and the good Intel chips are not really aligned with people on a budget.
I have 2 kids i had to build machines for and I am on a budget. All three of the machines in my house are the A10-7850k and so far i could not be happier. As soon as DX12 comes out i expect to be even happier when the kids birthdays come out and i can put a true gaming discrete card in and get extra performance than just the discrete card running solo.
With the A10-7870 out now prices are falling fast on the previous flagship and to be honest for the games i play i get good graphics as is. I play MechWarrior Online without issue, SWTOR, Smite, League of Legends, CS:GO and many others. I am not saying they are mind blowing graphics but all are playable. League maxed, Smite maxed, With AA and Shadows turned down almost all of the titles are at least medium settings.
Remember, budget gaming is the order of day here. Save up and then drop your discrete card in at a later date.
AMD A10-7850K Kaveri 12 Compute Cores (4 CPU + 8 GPU) 3.7GHz Socket FM2+ 95W $129.00
http://www.newegg.com/Product/Product.aspx?Item=N82E16819113359
I also have used the ASUS A88XM-A Board (around $75.00) in one of my builds and it works fine over a year later. But you may have your own preference. You will need a FM2+ board.