I was curious what Age of Empires needed. So, I did a bit of backward regression looking at old gpu benchmarks. For 60fps at 1080p, you'd need an 8800GTX. Today, that equates to a HD 5570/6570. The gpu in the A8-3850 is the 6550D and it performs somewhere between an HD 6450 and an HD5570/6570. Call it 15% slower, or 51fps. The gpu in the A6-3500, 6530D, is about 80% of the 6550D. So, about 40fps. The A4-3400's GPU has 160 cores (half of the A6-3500), but runs faster at 600MHz vs 443MHz. So, maybe 26fps.
So, yeah. Probably playable with the gpu in the A4.
The E-350 has 80 GPU cores running at 500MHz. So, not playable at 1080p. Might be playable (guessing 20fps) if you drop the resolution to 720p.
So, the E-350 *might* work for your needs. But, if you end up needing a discrete GPU, you'll need another case. The ISK-100 doesn't have room for a card.
I'd lean toward the G620
Pentium for $70 and an H61 motherboard for $70-90. If you wanted to up the performance a bit, go with the i3-2105
If it turns out you need a discrete GPU for your light gaming, a fanless 6570 runs $70, the 6670 ~$100.