If you're in the US/UK and you're going to use the 7770 then you could get an Athlon 750k/760k and a compatible FM2/FM2+ mobo which is basically an A10-5700/5800k without the APU (if you're outside then you'd probably have to order one of them through Amazon)
For upgradability sake the G3220 would be the better choice since you can eventually get that i5 down the line
At its price point the G3220 isn't a bad choice, though the 750k/760k are the usual recommendations at that price (though there's virtually no upgradability)
And since you're mostly playing DotA 2 and probably some less intensive games at this time (Crysis 3, Planetside 2 etc. would be playable still, just not very well) I'd say it'd be a good choice