I'd have to agree with herulach. My concern with going the Intel route would be the horribly overpriced processors compared with what you get with AMD. The GPU on something like an A10 would be more than enough for most games. Even the A8 is no slouch.
Of course, it's always better to go for a seperate CPU/GPU combination but if you're on a budget (if you're looking at an i3 then it's pretty clear that you are) then you should seriously consider an AMD APU. The only problem at the moment is that FM2+ is just around the corner, so if you go for an FM2 board it's unlikely that AMD will be releasing any new FM2 APUs, so the current A10 may be the highest you can go.
Whenever I've been asked to build a PC for someone, I've always suggested getting the best motherboard you can afford and then build your PC around it, even if it means getting the cheapest CPU you can find for now. With FM2+ around the corner, it makes FM2 a bit redundant if you're planning on upgrading at some point. So my usual advice doesn't really hold at the moment.