You haven't specified the PURPOSE of the machine.
1) Refurbished can be okay, but I don't recommend them. I don't think the small cost savings justify the potential issues.
2) There are some really great $400 laptops as well that I recommend even to primarily desktop users. You can still hookup to a monitor and use without it's screen. You also get a battery of course so it won't crash in a power outage.
3) You can't build a PC anyway for $400 that's a good value. Windows alone costs about $100 when bought separately.
4) If you want light-gaming your best bet is an APU, if you don't care about even light gaming I'd get a laptop or desktop with an Intel i5 CPU.
Here's a nice $400 laptop with a 17" screen: http://m.bestbuy.com/m/e/product/detail.jsp?skuId=2854029&pid=1219079079760&pcatId=pcmcat247400050000
Here's the APU equivalent. It's difficult to compare but I think the CPU portion might be slightly weaker than the Intel but the graphics might be slightly better on average:http://m.bestbuy.com/m/e/product/detail.jsp?skuId=2287004&pid=1219071221794&ev=prodView
Best time of year?
When the big sales are on.
However, to get a good sale on a computer you generally need to know what you want and possibly camp out to get a good deal. Also, keep in mind the crappier or poorer selling items are often the first to be discounted.
The real big advantage to the desktop is the possibility to upgrade the graphics, in which case I'd get an INTEL CPU system, and definitely not an APU. Other than that, there aren't a lot of choices, but I recommend Windows 8 regardless of what system you buy.
Great OS, however I also use START8 from Stardock (tweak the settings). It's only $5. This avoids the new interface which I dislike.