Strong reason: cost.I see no strong reason to go with an ATX midtower. It will be mostly empty. At least do miniITX.
Added a different microATX case that comes with a PSU for same price but NO mail-in rebate. This PSU should be no problem yes? (I see this one isn't bronze-rated, just efficiency rating).
2. The AMD APU is a CPU with integrated graphics processor. The Intel CPUs also have integrated graphics processors, but unless it is one of the highest end intel IGPs, they tend to be less powerful than the AMD offerings. However you sacrifice some CPU performance, so it's a trade off. However, if you have a micocenter close by, you might be able to get a better deal. Currently Micocenter offers the A10-6800K (quad core 4.1ghz) with the Gigabyte GA-F2A58M-HD2 motherboard for $120, which is about the same price as your current intel CPU/motherboard. However the A10-6800k has a MUCH more powerful GPU. http://www.anandtech.com/bench/product/1262?vs=1256 It goes toe to toe with the G3420 in CPU aspects, but as you can see the G3420 can't keep up in the graphics department. However depending on your mothers usage, you may not care about graphics performance. Both should be able to do HD youtube no problem.
Some people dissed the HEC-made ThermalTake TR2-430 430W PSUs, but they were always reliable for me. I ditched mine because people on the forums said that they were crap, so I bought some Antec BP500 "Basiq" units, and had to replace one after a year because the cheap fan went bad and was making grinding sounds. (The TR2-430's dual 80mm fans were silent for 3 years.) I bought some Antec EarthWatts 650W (made by Delta), I and a friend still have ours running reliably, nearly 5-6 years later. I also have a pair of Antec VP-450 PSUs that have been running for 3-4 years quite reliably. I also have some EarthWatts 500W units that have sat on the shelf for some years, broke one out recently for a G3258 build.
Edit: Though I agree with your comment about getting 8GB of RAM.
Plus this A10-7850 is a quad core. This is another CPU from AMD that does however use the module designs which is more than hyperthreading but not as good as true full cores actually are. However if you are able to get this CPU for the same cost as some of the other processor you were looking at then it might very well be a much nicer choice with obviously a much more powerful GPU. This is actually the top of the line APU from their last generation of APUs so it probably outperforms at least the lower end of the I3s as far as CPU power and probably outperforms most if not all I3s for GPU power and also GPGPU compute.
7850 is pretty respectable: http://www.anandtech.com/bench/product/1200?vs=1192 Matches a middle-i3 in MT loads (give or take), 2/3 of the single-threaded performance but packs a much stronger iGPU. Unfortunately, that iGPU is likely to sit idle its entire life, it won't be overclocked, and the APU is more expensive. Between the two, my vote goes to the i3 for this build.
The PC sitting next to me is about 1/10 the size of what a lot of you are suggesting, and costs less too:
Antec ISK110-VESA ITX case: $58
MSI H81I: $65
4GB of Crucial DDR3-1600: $40
Crucial MX100 128GB SSD : $70
Pentium G3258: $70
That's $303. All from Amazon.
OP, seriously, if you'd like to give your mom something that she'll be blown away by, this is it.
And for goodness sake, 8GB in a mom-puter? I challenge any one of you to give me a scenario in which she's going to notice the difference.
Longevity. I'd expect more than a plain old dual core with 4GB of RAM in 2015 if you want the box to last. mini-ITX has no expansion for upgrades either, even in a basic box, you want some headroom for upgrades hence standard ATX. I've built in that case too, its horrible if you have fat hands.
What kind of upgrades? New motherboard/processor? More RAM?
Whichever. You have options.
I can't think of any upgrades I'd want to put in a PC for my parents that would fit in an ATX midtower and wouldn't fit in a mini ITX case. Some of them fit standard ATX power supplies, while others use external power bricks. Seems like wasted space.
Think long term. I'd expect this build to last at least 5yrs, for that timeframe I'd definitely spend an extra $30 to $40 on an i3 as well as a decent H97 board.
The i3 I can sort of understand, software gets more bloated over time, but in terms of platform features, what would make an H97 more valuable than an H81, five years from now? I guess I fail to see the point. Unless you are suggesting that there will be no other SATA SSDs on the market in five years, that they will all be M.2 or SATAExpress?
I always overspec (to a degree, its not like you need a 5960X here :awe, a decent H97 board can be onsold or repurposed, but a $50 H81 frisbee (if it even lasts 5yrs) with limited ports and slots is useless.