An A10 can't beat the HD 530. Integrated GPUs just suck in general. If you want the cheapest option, sure - go AMD. I haven't since the Athlon 64 era, and I'm quite pleased with my choices.
That article doesn't say what you think it does. The AMD chip beat the HD 530 in all tests except the synthetic benchmark and WoW
at low detail settings. Once you turn up the detail, Intel can't keep up.
Not to mention, the cheapest chip with HD 530 graphics, which I think is the i3-6100, is only dual-core. While it might have better single-threaded CPU performance than an A10, it won't be as good at multitasking or running programs that take advantage of parallelism.
But it looks like most of the computers that I'm looking to buy (prebuilt). Don't have this SSD, they are all regular hard drives. What am I missing, is the SSD a regular hard drive or is it like a flash drive?
Let me put it this way: you want an SSD. You could build the
entire computer on a $200 budget, with $50-75 of that being the SSD, and it will be good for office productivity stuff. (And older games, for that matter -- think Morrowind instead of Skyrim.)
In contrast, even a much more expensive computer with a spinning-disc hard drive will feel slow in comparison.
Is the major thing I'm missing a video card? Is that what will make this more game friendly?
It depends on what you want to play. For a game like Skyrim, yes, you want a discrete graphics card. (And in turn, a discrete graphics card means Intel makes sense -- at least for the i5 like Thegoblinchief recommended. An i7 is still overkill and an unnecessary expense.)
For older games, an AMD with integrated graphics -- but
not an Intel with integrated graphics, as I explained above -- will be your most cost-effective option. As a bonus, older games are cheap so you win that way, too.
Also, I do have access to old machines that I can take apart. But I'm not sure if the motherboard is even worth salvaging. They are all 4-5 year old machines. Our office got new machines a few years ago.
Depends. If they're old Intel Pentium 4 / Netburst-architecture (which I'm not sure was even still around 4-5 years ago), maybe not. Otherwise, probably. They'll likely work fine for office-productivity, but would need a graphics card added for gaming (in which case you'd want to check to make sure they had a free PCIe x16 slot and correct auxiliary power connectors).